Puerto Rico Insurance Excise Tax Exemption Act of 2021 This bill exempts from the foreign insurer excise tax certain insurance policies, indemnity bonds, annuity contracts, or reinsurance policies issued by partnerships or corporations created or organized under the laws of a U.S. territory or possession. The exemption applies unless any of the covered hazards, risks, losses, or liabilities are also covered by a reinsurance policy issued by a foreign insurer or reinsurer other than the partnership or corporation.