Native American Housing Assistance and Self-Determination Reauthorization Act of 2021 This bill provides federal housing assistance to Indians and Native Hawaiians. Specifically, the bill reauthorizes through FY2032 and otherwise revises the Indian Housing Block Grant program and the Native Hawaiian Housing Block Grant program. Among other revisions to these programs, the bill expands allowable housing activities under the Indian program to include education-related stipends, college housing assistance, and other education-related assistance for low-income college students. Next, the bill authorizes the Department of Housing and Urban Development (HUD) to guarantee housing loans for Indians and Native Hawaiians through FY2032. HUD may make grants to eligible recipients of block grants for use in eliminating drug-related and violent crime. Additionally, the bill provides statutory authority for the Tribal HUD-VASH program, which provides rental assistance and supportive services to Indian veterans who are homeless or at risk of homelessness and living in or near an area where a tribe or tribally designated housing entity provides assistance for affordable housing. HUD must use at least 5% of rental assistance amounts under the HUD-VASH program, which provides housing assistance to homeless veterans, for the Tribal HUD-VASH program. The Tribal HUD-VASH program must be carried out by HUD in conjunction with the Department of Veterans Affairs. Under the program, grants must be made to entities eligible for housing assistance block grants. HUD may make renewal grants to entities that have received prior program grants.