Ensuring a Long-Term Housing Recovery Act of 2021 This bill increases the authorization of appropriations for the Department of Housing and Urban Development (HUD) to provide additional rental housing choice voucher assistance. This assistance may be used for rent, utilities (including internet service), related debt, fees, deposits, and landlord incentive payments. The bill authorizes HUD to waive certain requirements related to this additional assistance. In addition, the bill extends HUD's existing authority to waive requirements related to this assistance program and other programs that HUD administers.