Require Evaluation before Implementing Executive Wishlists Act of 2021 or the REVIEW Act of 2021 This bill prohibits a final agency rule from taking effect until (1) the agency submits the rule to the Office of Information and Regulatory Affairs (OIRA), and (2) OIRA makes a determination as to whether the rule is a high-impact rule that may impose an annual cost on the economy of at least $1 billion. In addition, an agency must postpone the effective date of a high-impact rule until the final disposition of all actions seeking judicial review of the rule.