Exhibit 23.1

INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM’S CONSENT

We consent to the inclusion in this Registration Statement of Haymaker Acquisition Corp. III on Form S-1 Amendment No. 1 [File No. 333-253010] of our report dated January 25, 2021, which includes an explanatory paragraph as to the Company’s ability to continue as a going concern, with respect to our audit of the financial statements of Haymaker Acquisition Corp. III as of December 31, 2020 and for the period from July 6, 2020 (inception) through December 31, 2020, which report appears in the Prospectus, which is part of this Registration Statement. We also consent to the reference to our Firm under the heading “Experts” in such Prospectus.

/s/ Marcum LLP

Marcum LLP

New York, NY

February 19, 2021