Amendment No. 1 to Investment Management Trust Agreement, dated December 4, 2024

Exhibit 10.1

AMENDMENT NO. 1 TO INVESTMENT MANAGEMENT

TRUST AGREEMENT

THIS AMENDMENT NO. 1 TO THE INVESTMENT MANAGEMENT TRUST AGREEMENT (this “Amendment”) is made as of December 4, 2024, by and between ESH Acquisition Corp., a Delaware corporation (the “Company”), and Continental Stock Transfer & Trust Company, a New York corporation (the “Trustee”). Capitalized terms contained in this Amendment, but not specifically defined in this Amendment, shall have the meanings ascribed to such terms in the Investment Management Trust Agreement made effective as of June 13, 2023, by and between the Company and the Trustee (the “Original Agreement”).

WHEREAS, the Company and the Trustee entered into the Original Agreement on June 13, 2023;

WHEREAS, Section 1(i) of the Original Agreement sets forth the terms that govern the liquidation of the Trust Account under the circumstances described therein;

WHEREAS, at a special meeting of the Company held on December 3, 2024, the Company’s stockholders approved (i) a proposal to give the Company the right to extend the date before which the Company must complete an initial Business Combination from December 16, 2024 for up to 12 additional one-month periods (ultimately no later than December 16, 2025) and (ii) give the Company the right to extend the date on which the Trustee must liquidate the Trust Account if the Company has not completed its initial Business Combination by December 16, 2024, for up to 12 additional one-month periods (and ultimately no later than December 16, 2025) (collectively, the “Extension”);

WHEREAS, holders of at least sixty-five percent (65%) of the issued and outstanding shares of Common Stock and Class B Common Stock, voting as a single class, approved the Extension Amendment and the Trust Amendment; and

WHEREAS, the parties desire to amend the Original Agreement to, among other things, reflect amendments to the Original Agreement contemplated by the Trust Amendment.

NOW, THEREFORE, in consideration of the mutual agreements contained herein and other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, and intending to be legally bound hereby, the parties hereto agree as follows:

1. Amendment to Trust Agreement. Section 1(i) of the Original Agreement is hereby amended and restated in its entirety as follows:

“(i) Commence liquidation of the Trust Account only after and promptly after (x) receipt of, and only in accordance with, the terms of a letter from the Company (“Termination Letter”) in a form substantially similar to that attached hereto as either Exhibit A or Exhibit B, as applicable, signed on behalf of the Company by its Chief Executive Officer, President, Secretary or Chairman of the board of directors of the Company (the “Board”) or other authorized officer of the Company, and, in the case of Exhibit A, acknowledged and agreed to by the Representative and the Co-Manager, and complete the liquidation of the Trust Account and distribute the Property in the Trust Account, including interest not previously released to the Company to pay its taxes, only as directed in the Termination Letter and the other documents referred to therein, or (y) upon the date which is the later of (1) December 16, 2024, as may be extended by the Company for up to 12 additional one-month periods (ultimately no later than December 16, 2025) (any such extended date, the “Extended Date”) upon the deposit into the Trust Account of the lesser of (x) $30,000 or (y) $0.05 per month for each public share that remains outstanding (and was not redeemed in connection with the Extension), for each calendar month (commencing on December 16, 2024 and on the 16^th day of each subsequent month) until the Extended Date, or portion thereof, that is needed to complete an initial Business Combination, such deposit(s) to be made within seven calendar days of December 16, 2024 or within seven calendar days of the 16^th day of such subsequent month, as applicable, and (2) such later date as may be approved by the Company’s stockholders in accordance with the Company’s amended and restated certificate of incorporation if a Termination Letter has not been received by the Trustee prior to such date, in which case the Trust Account shall be liquidated in accordance with the procedures set forth in the Termination Letter attached as Exhibit B and the Property in the Trust Account, including interest not previously released to the Company to pay its taxes (less up to $100,000 of interest that may be released to the Company to pay dissolution expenses), shall be distributed to the Public Stockholders of record as of such date. It is acknowledged and agreed that there should be no reduction in the principal amount per share initially deposited in the Trust Account;”

2. Exhibit B of the Trust Agreement is hereby amended and restated in its entirety as follows:

[Letterhead of Company]

[Insert date]

Continental Stock Transfer & Trust Company

One State Street, 30^th Floor

New York, NY 10004

Attn: Francis Wolf and Celeste Gonzalez

Re: Trust Account Termination Letter

Dear Mr. Wolf and Ms. Gonzalez:

Pursuant to Section 1(i) of the Investment Management Trust Agreement between ESH Acquisition Corp. (the “Company”) and Continental Stock Transfer & Trust Company (the “Trustee”), dated as of June 13, 2023 (the “Trust Agreement”), this is to advise you that the Company has been unable to effect a business combination with a Target Business within the time frame specified in the Company’s amended and restated certificate of incorporation, as described in the Company’s Prospectus relating to the Offering. Capitalized terms used but not defined herein shall have the meanings set forth in the Trust Agreement.

In accordance with the terms of the Trust Agreement, we hereby authorize you to liquidate all of the assets in the Trust Account and to transfer the total proceeds into a segregated account held by you on behalf of the Beneficiaries to await distribution to the Public Stockholders. The Company has selected [            ] (1) as the effective date for the purpose of determining when the Public Stockholders will be entitled to receive their share of the liquidation proceeds. You agree to be the Paying Agent of effective and, in your separate capacity as Paying Agent, agree to distribute said funds directly to the Company’s Public Stockholders in accordance with the terms of the Trust Agreement and the amended and restated certificate of incorporation of the Company. Upon the distribution of all the funds, net of any payments necessary for reasonable unreimbursed expenses related to liquidating the Trust Account, your obligations under the Trust Agreement shall be terminated, except to the extent otherwise provided in Section 1(i) of the Trust Agreement.

3. Miscellaneous Provisions.

3.1. Successors. All the covenants and provisions of this Amendment by or for the benefit of the Company or the Trustee shall bind and inure to the benefit of their permitted respective successors and assigns.

3.2. Severability. This Amendment shall be deemed severable, and the invalidity or unenforceability of any term or provision hereof shall not affect the validity or enforceability of this Amendment or of any other term or provision hereof. Furthermore, in lieu of any such invalid or unenforceable term or provision, the parties hereto intend that there shall be added as a part of this Amendment a provision as similar in terms to such invalid or unenforceable provision as may be possible and be valid and enforceable.

3.3. Applicable Law. This Amendment shall be governed by and construed and enforced in accordance with the laws of the State of New York.

3.4. Counterparts. This Amendment may be executed in several original or facsimile counterparts, each of which shall constitute an original, and together shall constitute but one instrument.

3.5. Effect of Headings. The section headings herein are for convenience only and are not part of this Amendment and shall not affect the interpretation thereof.

3.6. Entire Agreement. The Original Agreement, as modified by this Amendment, constitutes the entire understanding of the parties and supersedes all prior agreements, understandings, arrangements, promises and commitments, whether written or oral, express or implied, relating to the subject matter hereof, and all such prior agreements, understandings, arrangements, promises and commitments are hereby canceled and terminated.

[Signature page follows]

IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be duly executed as of the date first above written.

Continental Stock Transfer & Trust Company, as Trustee

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