Providing Retrospective Observations Validating Economics and Increasing Transparency Act of 2021 or the PROVE IT Act of 2021 This bill requires agencies, when publishing a final major rule and biennially thereafter, to assess the impact of the rule on regulated entities, determine how the actual benefits and costs of the rule have varied from those anticipated, and assess the effectiveness of the rule at meeting its regulatory objectives. If an agency determines that the cost to regulated entities has exceeded the anticipated cost, then the agency must assess and report whether the rule is meeting its objectives and whether the rule is necessary. Further, in such case, the agency must reopen the public comment period for 60 days and consider modifications or alternatives to the rule. The bill defines a major rule as a rule likely to cause (1) an annual effect on the economy of $100 million or more; (2) a major increase in costs or prices; or (3) significant adverse effects on competition, employment, investment, productivity, innovation, or the ability of U.S.-based enterprises to compete with foreign-based enterprises.