Exhibit 10.1

October 16, 2025

Star Equity Fund, LP
c/o Jeffrey E. Eberwein
53 Forest Avenue, Suite 101
Old Greenwich, Connecticut 06870

Re: Gyrodyne, LLC

Dear Mr. Eberwein:

This letter agreement is intended to memorialize the understandings and agreements that have been reached between Gyrodyne, LLC (the “Company” or “we”) and Star Equity Fund, LP (collectively with its Affiliates (as defined below), “Star Equity”) relating to, among other things, Star Equity’s notice to the Company (the “Nomination Notice”) of its intent to nominate two candidates for election to the Company’s board of directors (the “Board”) at the Company’s 2025 annual meeting of shareholders (the “Annual Meeting”).

In consideration of the promises, representations and mutual covenants and agreements set forth herein, and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the Company and Star Equity have successfully reached the following agreements:

1.    Effective upon execution of this letter agreement, Star Equity shall irrevocably withdraw the Nomination Notice (with this letter agreement deemed to evidence each such withdrawal), and shall cease any and all solicitation and other activity in connection with the Annual Meeting.

2.    Until the Termination Date (as defined below), Star Equity shall not directly or indirectly (a) nominate, recommend for nomination or give notice of an intent to nominate or recommend for nomination a person for election at any meeting of shareholders of the Company at which directors are to be elected; (b) initiate, encourage or participate in any solicitation of proxies in respect of any election contest or removal contest with respect to directors of the Company; (c) submit, initiate, make or be a proponent of any shareholder proposal for consideration at, or bring any other business before, any meeting of shareholders of the Company or shareholder actions by written consent in lieu of a meeting of shareholders; (d) initiate, encourage or participate in any solicitation of proxies in respect of any shareholder proposal for consideration at, or other business brought before, any meeting of shareholders of the Company or shareholder actions by written consent in lieu of a meeting of shareholders; (e) initiate, encourage or participate in any “withhold” or similar campaign with respect to any meeting of shareholders of the Company or shareholder actions by written consent in lieu of a meeting of shareholders; (f) make any public or private proposal (other than to the Board), public statement or otherwise seek to encourage, advise or assist any person in, (i) any change in the number or term of directors serving on the Board or the filling of any vacancies on the Board, (ii) any change in the Company’s business, operations, strategy, management, governance, corporate structure or other affairs or policies, (iii) causing a class of securities of the Company to be delisted from, or cease to be authorized or quoted on, any securities exchange or (iv) causing a class of equity securities of the Company to become eligible for termination of registration pursuant to Section 12(g)(4) of the Securities Exchange Act of 1934, as amended, and the rules and regulations promulgated thereunder, (the “Exchange Act”); or (g) enter into any discussions, negotiations, agreements or understandings with any person with respect to any action Star Equity is prohibited from taking pursuant to subclauses (a) through (f) above, or advise, assist, encourage or persuade any person to take any such action.

3.    The Company agrees that the Board and all necessary and applicable committees of the Board shall take all necessary actions to nominate Richard B. Smith, and no other individual(s), as a director for election to the Board at the Annual Meeting with a term expiring at the Company’s 2028 annual meeting of shareholders, to serve until his successor has been duly elected and qualified, or until Mr. Smith’s earlier death, resignation or removal.

4.    If, from the date hereof until the Termination Date, in the event that one of Jan H. Loeb, Nader G.M. Salour, Richard B. Smith or Ronald J. Macklin (each, a “Continuing Director”) resigns as a director or ceases to be a director due to death or disability, then the Board and Star Equity shall engage in good faith discussions to identify a mutually acceptable independent (as defined in the listing rules of the NASDAQ Stock Market LLC) director (the “Replacement Director”) to be appointed to the Board to fill the Board seat vacated by such applicable Continuing Director; provided, that, for the avoidance of doubt, Star Equity shall have replacement rights with respect to the first applicable Continuing Director and no replacement rights with respect to the remaining Continuing Directors; provided, however, that in the event the Replacement Director, or his replacement (as the case may be), resigns as a director or ceases to be a director due to death or disability prior to the Termination Date, then the Board and Star Equity shall engage in good faith discussions to identify a mutually acceptable independent (as defined in the listing rules of the NASDAQ Stock Market LLC) director to fill the Board seat vacated by such Replacement Director. Any rights or obligations of the Board and Star Equity as provided in this Section 4 shall terminate on the Termination Date. In the event a Replacement Director cannot be agreed upon, then the size of the Board shall be reduced to three directors. In the event that a remaining Continuing Director subsequently resigns as a director or ceases to be a director due to death or disability at a time when the Board and Star Equity have not agreed upon a Replacement Director for such first applicable Continuing Director, then the Board shall make no additional appointments until the Board and Star Equity identify a mutually acceptable Replacement Director as provided in this Section 4.

5.    From the conclusion of the Annual Meeting until the Termination Date, the size of the Board shall not exceed four directors.

6.    The Company agrees not to increase Board fees, and shall limit the aggregate fee paid to the Chairperson of the Board to $65,000.

7.    For the avoidance of doubt, Star Equity shall not, directly or indirectly, cause or influence any of its Affiliates or Associates (as defined in Rule 12b-2 of the Exchange Act) (respectively, “Affiliates” and “Associates”) to take any action that, if taken by Star Equity, would constitute a violation or breach of any term or condition of this letter agreement.

8.    The Company shall issue a press release (the “Press Release”) in a form prepared by the Company and approved by Star Equity (such approval not to be unreasonably withheld), announcing entry into this letter agreement. Prior to the issuance of the Press Release, neither party shall make any public announcement regarding this letter agreement without the prior written consent of the other party, except to the extent required by applicable law or the applicable securities exchange.

9.    No later than four business days following the execution of this letter agreement, the Company shall file with the U.S. Securities and Exchange Commission (the “SEC”) a Current Report on Form 8-K reporting its entry into this letter agreement and appending this letter agreement as an exhibit thereto. No later than two business days following the execution of this letter agreement, Star Equity shall file with the SEC an amendment to its Schedule 13D reporting its entry into this letter agreement and appending this letter agreement as an exhibit thereto. Each party shall provide the other party with a reasonable opportunity to review and comment on its applicable SEC filing prior to such respective report or schedule being filed and consider in good faith any comments of the other party.

10.    The term of this letter agreement will commence on the date hereof and shall continue until December 31, 2026 (the “Termination Date”); provided, however, that the Termination Date shall be delayed until December 31, 2027, if the Board re-nominates both Messrs. Loeb and Salour for election at the Company’s 2026 annual meeting of shareholders and both Messrs. Loeb and Salour agree to such re‑nomination; provided, further, that any party (the “Non-Breaching Party”) may earlier terminate this letter agreement if the other party commits a breach of this letter agreement (the “Breaching Party”) that is not cured within fifteen days after the Breaching Party’s receipt of written notice from the Non‑Breaching Party or, if impossible to cure within fifteen days, which the Breaching Party has not taken any substantive action to cure within such fifteen-day period.

11.    Until the Termination Date, Star Equity shall vote, or cause to be voted (including, without limitation, any action by written consent), all of its common shares of limited liability company interests beneficially owned, at all meetings of the Company’s shareholders in accordance with the Board’s recommendation in connection with any and all proposals, including, without limitation, those related to the election, removal or replacement of any director; provided, however, that (a) Star Equity shall be permitted to vote in its sole discretion on any proposal of the Company in respect of any equity tender offer, equity exchange offer, merger, acquisition, joint venture, business combination, financing, recapitalization, reorganization, restructuring, disposition, distribution, or other transaction with a third party that, in each case, would result in a change of control of the Company, liquidation, dissolution or other extraordinary transaction involving a majority of its equity securities or a majority of its assets (determined on a consolidated basis), and, for the avoidance of doubt, including, without limitation, any such transaction with a third party that is submitted for a vote of the Company’s shareholders, and (b) as to any special meeting occurring after the Annual Meeting, Star Equity shall be permitted to vote in accordance with the recommendation of Institutional Shareholder Services Inc. (“ISS”) where the recommendation of ISS differs from the Board’s recommendation on any matter other than the nomination of directors.

12.    The Company shall promptly reimburse Star Equity for the expenses incurred by Star Equity in connection with the Annual Meeting and the subject matter of this letter agreement, including, without limitation, the negotiation and execution of this letter agreement and the transactions contemplated hereby, in the amount of $25,000. Such amount shall be paid to Star Equity promptly following the execution of this letter agreement.

13.    Until the Termination Date, except for such truthful statements as may be required by applicable law or the rules of any self-regulatory organization, Star Equity will not make, or permit any of its Representatives (as defined below) to make, or cause a third party to make, any public statement that disparages, or is otherwise negative or critical of the Company, its Affiliates or any of the Company’s past or current directors or officers, and the Company will not make, or permit any of its Representatives to make, or cause a third party to make, any public statement that disparages, or is otherwise negative or critical of Star Equity, its Affiliates, or their directors or officers. “Representatives” means (a) a person’s Affiliates and Associates and (b) its and their respective directors, officers, employees, partners, members, managers, consultants, legal or other advisors, agents and other representatives acting in a capacity on behalf of, in concert with or at the direction of such person or its Affiliates or Associates; provided, that when used with respect to the Company, “Representatives” shall not include any non-executive employees.

14.    Each party acknowledges and agrees that irreparable harm to the other party may occur in the event any of the provisions of this letter agreement are not performed in accordance with their specific terms or are otherwise breached and that such injury would not be adequately compensable by the remedies available at law (including, without limitation, the payment of money damages). Accordingly, each party will be entitled to specifically enforce the covenants and other agreements of the other party contained in this letter agreement and to obtain injunctive relief restraining the other party from breaching or threatening to breach this letter agreement, and the other party will not take action, directly or indirectly, in opposition to the party seeking such relief on the grounds that any other remedy or relief is available at law or in equity. The parties further agree to waive any requirement for the security or posting of any bond in connection with any such relief. The prevailing party that obtains a final, non-appealable order shall be entitled to recover its fees and expenses incurred with respect to any action from the non-prevailing party. The remedies available pursuant to this Section 14 shall not be deemed to be the exclusive remedies for a breach of this letter agreement but shall be in addition to all other remedies available at law or equity.

15.    Each party represents and warrants that it is duly authorized and has legal capacity to execute and deliver this letter agreement. Each party represents and warrants to the other parties that the execution and delivery of this letter agreement and the performance of such party’s obligations hereunder have been duly authorized and that this letter agreement is a valid and legal agreement binding on such party and enforceable in accordance with its terms.

16.    Any notices required or permitted to be given under this letter agreement shall be in writing and shall be delivered by overnight courier or electronic mail with confirmation of receipt to the addresses specified on the signature page of this letter agreement.

17.    This letter agreement may be executed in one or more counterparts, each of which shall be deemed an original, but all of which together shall constitute one and the same agreement. Signatures to this letter agreement transmitted by electronic mail shall have the same effect as physical delivery of the paper document bearing the original signature. No modifications of this letter agreement can be made except in writing signed by each of the parties. Unless required to be disclosed by federal or state securities or other laws, the parties agree to keep this letter agreement confidential.

18.    If any provision of this letter agreement is held invalid or unenforceable by any court of competent jurisdiction, the other provisions shall remain in full force and effect and shall in no way be affected, impaired or invalidated. Any provision held invalid or unenforceable only in part or degree shall remain in full force and effect to the extent not held invalid or unenforceable. The parties further agree to replace such invalid or unenforceable provision with a valid and enforceable provision that will achieve, to the extent possible, the purposes of such invalid or unenforceable provision.

19.    This letter agreement and all disputes or controversies out of or related to this letter agreement shall be deemed to be made under the laws of the State of New York and for all purposes shall be governed by, and construed in accordance with, the laws of such State applicable to contracts to be made and performed entirely within such State, without reference to conflicts of laws principles.

If the foregoing accurately sets forth our agreements, please sign this letter agreement where indicated below.

Address for Notices for Star Equity:

Star Equity Fund, LP
c/o Jeffrey E. Eberwein
53 Forest Avenue, Suite 101
Old Greenwich, Connecticut 06870
Email: jeff.eberwein@starequity.com

Exhibit 10.2

Gyrodyne, LLC
One Flowerfield, Suite 24
Saint James, New York 11780

October 17, 2025

Gyrodyne, LLC
Attn: Ronald J. Macklin, Nader G.M. Salour and Richard B. Smith
One Flowerfield, Suite 24
Saint James, New York 11780

Leap Tide Capital Management LLC
c/o Jan Loeb
2800 Quarry Lake Drive
Baltimore, Maryland 21209

Re:         Gyrodyne, LLC

Dear Messrs. Loeb, Macklin, Salour and Smith:

This letter agreement is intended to memorialize the understandings and agreements that we have reached with Leap Tide Capital Management LLC (collectively with its affiliates, “Leap Tide”) and each of you (together with Leap Tide, each a “Party” and collectively, the “Parties”) relating to, among other things, the composition of the Board of Directors (the “Board”) of Gyrodyne, LLC, a New York limited liability company (the “Company”).

We have successfully reached the following agreements:

1.     Until the Termination Date (as defined below), the Parties will appear in person or by proxy at each Shareholder Meeting and will vote or cause to be voted (including, without limitation, in any action by written consent) all Voting Securities beneficially owned, or deemed to be beneficially owned (as determined under Rule 13d-3 promulgated under the Securities Exchange Act of 1934, as amended), and entitled to vote as of the applicable record date, by the Parties: (a) in favor of the slate of directors recommended by the Board, and (b) otherwise in accordance with the Board’s recommendations with respect to any other properly vetted proposals submitted to the shareholders of the Company. Further, the Parties will, if requested by the Company, publicly (and in any engagement with shareholders and proxy advisory firms) and privately support the Company (including the Board), director nominations, proposals and/or announcements made by the Company, and solicit proxies in accordance with the Board’s recommendations with respect to the director nominations and proposals submitted at each Shareholder Meeting until the Termination Date (it being understood that such solicitation would not require the Parties to hire their own proxy solicitor at their own expense to solicit independently of the Company).

2.     The term of this letter agreement will commence on the date hereof and shall continue until the date that is thirty days prior to the opening of the advance notice period pursuant to the Company’s Amended and Restated Limited Liability Company Agreement for the submission of shareholder director nominations for the Company’s 2028 annual meeting of shareholders (the date of such termination, the “Termination Date”).

3.     Until the Termination Date, the Parties shall not:

4.     Each Party to this letter agreement will be entitled to specifically enforce the covenants and other agreements of the other Party or Parties contained herein and to obtain injunctive relief restraining the other Party or Parties from breaching or threatening to breach this letter agreement.

5.     Certain Defined Terms.

a.     “Shareholder Meeting” means each annual meeting or special meeting of shareholders of the Company and any meeting or action by written consent of the Company’s shareholders called or held in lieu thereof, and any adjournments, postponements, reschedulings and continuations thereof.

b.     “Voting Securities” means the Company’s common shares of limited liability company interests, par value $1.00 per share and any other securities of the Company entitled to vote in the election of directors.

6.     This letter agreement contains the entire agreement between the Parties and supersedes all other prior agreements and understandings, both written and oral, between the Parties hereto with respect to the subject matter hereof. No modifications of this letter agreement can be made except in writing signed by an authorized representative of each of the Parties.

7.     This letter agreement may be executed in one or more counterparts, each of which shall be deemed an original, but all of which together shall constitute one and the same agreement. Signatures to this letter agreement transmitted by electronic mail in “portable document format” (.pdf) or by other electronic means shall have the same effect as physical delivery of the paper document bearing the original signature.

8.     If any provision of this letter agreement is held invalid or unenforceable by any court of competent jurisdiction, the other provisions of this letter agreement shall remain in full force and effect and shall in no way be affected, impaired or invalidated. Any provision of this letter agreement held invalid or unenforceable only in part or degree shall remain in full force and effect to the extent not held invalid or unenforceable. The Parties further agree to use their commercially reasonable best efforts to replace such invalid or unenforceable provision of this letter agreement with a valid and enforceable provision that will achieve, to the extent possible, the purposes of such invalid or unenforceable provision.

9.     This letter agreement and all disputes or controversies out of or related to this letter agreement shall be deemed to be made under the laws of the State of New York and for all purposes shall be governed by, and construed in accordance with, the laws of such State applicable to contracts to be made and performed entirely within such State, without reference to conflicts of laws principles.

* * * * * *

If the foregoing accurately sets forth our agreements, please sign this letter agreement as indicated below.

ACKNOWLEDGED AND AGREED,
as of the date written above:

LEAP TIDE CAPITAL MANAGEMENT LLC


By:                                                                           
Name: Jan Loeb
Title: Managing Member

JAN LOEB

By:                                                                           
      Jan Loeb

Address for Notices for Leap Tide and Mr. Loeb:

2800 Quarry Lake Drive
Baltimore, Maryland 21209

RONALD J. MACKLIN

By: Ronald J. Macklin Address for Notices for Mr. Macklin: Gyrodyne, LLC Attn: Ronald J. Macklin One Flowerfield, Suite 24 Saint James, New York 11780 By: Nader G.M. Salour Address for Notices for Mr. Salour: Gyrodyne, LLC Attn: Nader G.M. Salour One Flowerfield, Suite 24 Saint James, New York 11780

NADER G.M. SALOUR

RICHARD B. SMITH

By:                                                                        
      Richard B. Smith


Address for Notices for Mr. Smith:

Gyrodyne, LLC
Attn: Richard B. Smith
One Flowerfield, Suite 24
Saint James, New York 11780

Exhibit 99.1

Press Release

Gyrodyne Announces Agreement with Star Equity Fund

Agrees to Board Size Reduction and Certain Director Compensation Limitations;

Star Equity Withdraws Nominations

St. James, N.Y., October 17, 2025 /Newswire/ -- Gyrodyne, LLC (Nasdaq: GYRO), an owner and manager of a diversified portfolio of real estate properties (“Gyrodyne”), today announced that it has entered into an agreement (the “Agreement”) with Star Equity Fund, LP (“Star Equity Fund”), under which Star Equity Fund has withdrawn its slate of nominees for election at the 2025 annual shareholders meeting, and Gyrodyne will reduce the size of its board from five to four directors, freeze director compensation and limit the aggregate fee paid to the Chairman to $65,000. In connection with the reduction in board size, Richard Smith will be the sole nominee standing for election at the 2025 annual shareholders meeting.

Star Equity has also agreed to certain customary standstill provisions. The full agreement with Star Equity will be filed in a Current Report on Form 8-K with the Securities and Exchange Commission.

The agreement with Star Equity Fund reflects Gyrodyne’s continued commitment to constructive engagement with shareholders as part of its ongoing efforts to strengthen governance, enhance transparency and drive long-term value creation for all shareholders.

Gary Fitlin, Gyrodyne’s President and Chief Executive Officer, stated that “We appreciate the thoughtful input from Star Equity and our broader shareholder base. Their perspectives have strengthened our efforts as we work toward completing the sale of our properties and delivering maximum value to our shareholders.”

Jeff Eberwein, manager of Star Equity Fund, added that “Following the most recent constructive discussions with the company, we are pleased to have worked collaboratively with the Board to enhance governance and further align with shareholders’ interests”.

Nader Salour, Chairman of Gyrodyne’s Nominating Committee, also added: “On behalf of the entire company and Board of Directors, I want to express our deep gratitude to Paul Lamb for his extraordinary 28 years of service to Gyrodyne. His steady leadership and strategic vision have been instrumental in guiding the company through periods of tremendous challenge and transformation. Paul Lamb leaves behind a lasting legacy of integrity and a steadfast commitment to our stakeholders. While he will not be standing for re-election at the upcoming shareholders’ meeting, as a significant shareholder he will continue to be an important voice and valued supporter of the company’s long-term success. We thank him for his many contributions and wish him the very best in the years ahead.”

About Gyrodyne, LLC

Gyrodyne, LLC owns and manages a diversified portfolio of real estate properties comprising office, industrial and service-oriented properties in the New York metropolitan area. The Company owns a 63 acre site approximately 50 miles east of New York City on the north shore of Long Island, which includes industrial and office buildings and undeveloped property, and a medical office park in Cortlandt Manor, New York, both of which are the subject of plans to seek value-enhancing entitlements. The Company’s common shares are traded on the NASDAQ Stock Market under the symbol GYRO. Additional information about the Company may be found on its web site at www.gyrodyne.com.

Forward-Looking Statements

The statements made in this press release that are not historical facts constitute "forward-looking information" within the meaning of the Private Securities Litigation Reform Act of 1995, and Section 27A of the Securities Act of 1933 and Section 21E of the Securities Exchange Act of 1934, both as amended, which can be identified by the use of forward-looking terminology such as "may," "will," "anticipates," "expects," "projects," "estimates," "believes," "seeks," "could," "should," or "continue," the negative thereof, other variations or comparable terminology as well as statements regarding the evaluation of strategic alternatives. Important factors, including certain risks and uncertainties, with respect to such forward-looking statements that could cause actual results to differ materially from those reflected in such forward-looking statements include, but are not limited to, risks and uncertainties generally relating to our efforts to enhance the values of our remaining properties and seek the orderly, strategic sale of such properties as soon as reasonably practicable, risks associated with the Article 78 Proceeding against the Company and any other litigation that may develop in connection with our efforts to enhance the value of and sell our properties, risks relating to our national marketing campaign led by JLL for the sale of our Flowerfield and Cortlandt Manor properties, risks associated with our purchase and sale agreement with B2K (and future purchase and sale agreements for our remaining properties that may be contingent on years-long regulatory contingencies) in light of our financial condition, community activism risk, proxy contests and other actions of activist shareholders, regulatory enforcement risk, risks inherent in the real estate markets of Suffolk and Westchester Counties in New York, the potential residual effects of the COVID-19 pandemic, lingering risks relating to the 2023 banking crisis and closure of two major banks (including one with whom we indirectly had a mortgage loan which the FDIC transferred in December 2023 to a new holder following the banks closure), ongoing inflation risk, ongoing interest rate uncertainty, recession uncertainty and supply chain constraints or disruptions, and other risks detailed from time to time in Gyrodyne’s SEC reports.

Contact:

Gary Fitlin

Chief Executive Officer

Gyrodyne, LLC

Phone: (631) 584-5400

gfitlin@gyrodyne.com

https://www.gyrodyne.com