EX-10.4





 Exhibit 10.4 

HAYMAKER ACQUISITION CORP. III 

501 Madison Avenue, Floor 12 

New York, NY 10022 

March 1, 2021 
 Mistral Capital Management
LLC 
 501 Madison Avenue, Floor 12 
 New York, NY 10022 

Re: Administrative Support Agreement 

Ladies and Gentlemen: 
 This letter agreement by
and between Haymaker Acquisition Corp. III (the “Company”) and Mistral Capital Management LLC (“Mistral”), dated as of the date hereof, will confirm our agreement that, commencing on the date the securities of the
Company are first listed on The Nasdaq Capital Market (the “Listing Date”), pursuant to a Registration Statement on Form S-1 and prospectus filed with the U.S. Securities and Exchange
Commission (the “Registration Statement”) and continuing until the earlier of the consummation by the Company of an initial business combination or the Company’s liquidation (in each case as described in the Registration
Statement) (such earlier date hereinafter referred to as the “Termination Date”): 
 (i) Mistral shall make available, or
cause to be made available, to the Company, at 501 Madison Avenue, Floor 12, New York, NY 10022 (or any successor location of Mistral), certain office space, utilities and secretarial and administrative support as may be reasonably required by the
Company. In exchange therefor, the Company shall pay Mistral the sum of $20,000 per month on the Listing Date and continuing monthly thereafter until the Termination Date; and 

(ii) Mistral hereby irrevocably waives any and all right, title, interest, causes of action and claims of any kind as a result of, or
arising out of, this letter agreement (each, a “Claim”) in or to, and any and all right to seek payment of any amounts due to it out of, the trust account established for the benefit of the public stockholders of the Company and
into which substantially all of the proceeds of the Company’s initial public offering will be deposited (the “Trust Account”) as a result of, or arising out of, this letter agreement, and hereby irrevocably waives any Claim it
may have in the future, which Claim would reduce, encumber or otherwise adversely affect the Trust Account or any monies or other assets in the Trust Account, and further agrees not to seek recourse, reimbursement, payment or satisfaction of any
Claim against the Trust Account or any monies or other assets in the Trust Account for any reason whatsoever. 
 This letter agreement
constitutes the entire agreement and understanding of the parties hereto in respect of its subject matter and supersedes all prior understandings, agreements, or representations by or among the parties hereto, written or oral, to the extent they
relate in any way to the subject matter hereof or the transactions contemplated hereby. 
 This letter agreement may not be amended,
modified or waived as to any particular provision, except by a written instrument executed by the parties hereto. 
 No party hereto may
assign either this letter agreement or any of its rights, interests, or obligations hereunder without the prior written approval of the other party. Any purported assignment in violation of this paragraph shall be void and ineffectual and shall not
operate to transfer or assign any interest or title to the purported assignee. 
 This letter agreement constitutes the entire relationship
of the parties hereto, and any litigation between the parties (whether grounded in contract, tort, statute, law or equity) shall be governed by, construed in accordance with, and interpreted pursuant to the laws of the State of New York, without
giving effect to its choice of law principles. 
 [Signature Page Follows] 

  
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	Very truly yours,
	
	HAYMAKER ACQUISITION CORP. III
		
	By:	 	 /s/ Steven J. Heyer

		 	Name: Steven J. Heyer
		 	Title: Chief Executive Officer


  

			
	AGREED TO AND ACCEPTED BY:
	
	MISTRAL CAPITAL MANAGEMENT LLC
		
	By:	 	 /s/ Christopher Bradley

	Name:	 	Christopher Bradley
	Title:	 	Managing Member

 [Signature Page to Administrative Support Agreement]