Holocaust Insurance Accountability Act of 2021 This bill allows a beneficiary (or an heir of a beneficiary) of certain insurance policies in effect during the Holocaust to sue in U.S. district court to enforce rights under such policies. An insurance policy covered under this bill must have been (1) in effect at any time between January 31, 1933, and December 31, 1945, and (2) issued to a policyholder domiciled in Nazi-controlled territory or Switzerland. A court shall award to a prevailing beneficiary (1) the amount due under a policy, (2) prejudgment interest of 6% a year, (3) attorney's fees and costs, and (4) treble damages if the insurer acted in bad faith. An action under this bill or state law related to a covered insurance policy shall be considered timely if filed within 10 years of this bill's enactment. Judgments and agreements entered before this bill's enactment shall not preclude a claim brought under the bill, with certain exceptions. Neither executive agreements between the United States and a foreign government nor U.S. executive foreign policies shall (1) affect or preclude claims brought under this bill, or (2) supersede or preempt any state laws relating to insurance policies covered by this bill.