Compass Therapeutics (CMPX) 8-K/A Independent Auditor’s Report

Exhibit 23.1

Consent of Independent Auditor

We consent to the incorporation by reference in the Registration Statement on Form S-3 (File No. 333-257821) of Compass Therapeutics, Inc. and the Registration Statement on Form S-8 (File No. 333-252103) pertaining to the 2020 Stock Option and Incentive Plan of Compass Therapeutics, Inc., of our report, which includes an explanatory paragraph relating to Trigr Therapeutics, Inc.’s ability to continue as a going concern, dated August 4, 2021 on our audit of the financial statements of Trigr Therapeutics, Inc. as of December 31, 2020 and for the year then ended, included in this Current Report on Form 8-K/A of Compass Therapeutics, Inc.

/s/ CohnReznick LLP

Hartford, Connecticut

August 4, 2021