Indian Programs Advance Appropriations Act of 2021 This bill authorizes advance appropriations for several covered appropriations accounts of (1) the Bureau of Indian Affairs and the Bureau of Indian Education within the Department of the Interior, and (2) the Indian Health Service within the Department of Health and Human Services. The advance appropriations provide new budget authority that first becomes available for the first fiscal year after the budget year. The covered accounts within the Bureau of Indian Affairs are (1) Operation of Indian Programs, (2) Contract Support Costs, (3) the Indian Guaranteed Loan Program, (4) Construction, and (5) Payments for Tribal Leases. The covered accounts within the Bureau of Indian Education are (1) Operation of Indian Education Programs, and (2) Education Construction. The covered accounts within the Indian Health Service are (1) Indian Health Services, (2) Contract Support Costs, (3) Payments for Tribal Leases, and (4) Indian Health Facilities. The bill also requires the President's budget and the supporting documents submitted to Congress to include detailed estimates related to the advance appropriations.