Congressional Review of Agency Legal Settlements Act of 2021 This bill requires federal agencies to submit certain settlement agreements to Congress and allows Congress to disapprove of such agreements. The bill applies to proposed voluntary compromise settlements that include (1) a financial award paid by an agency that is more than $10 million aggregated across all similarly situated cases or legal claims against the agency, or (2) an agreement to modify or alter an agency rule. Before an agency may enter into such an agreement, the agency must submit to Congress a report that includes specified information, such as the terms and class of claimants covered by the agreement. The bill (1) specifies the effect of passage of a joint resolution of disapproval related to such an agreement, and (2) provides for an expedited procedure for such resolutions.