Buy Green Act of 2021 This bill provides for federal procurement of clean energy products. Specifically, the bill establishes a Clean Energy Fund at the Department of Energy (DOE) and authorizes DOE to transfer amounts from the fund to federal agencies for clean energy-related purchases. The bill creates a grant program for state, local, and tribal governments to make such purchases. The bill (1) provides grants to electrify the federal vehicle fleet, to states and municipalities to electrify public transit and school buses, and to design, build, and retrofit buildings to be more energy efficient; and (2) establishes a grant program for U.S. companies to invest in clean energy manufacturing by retrofitting or building facilities that produce clean energy products. The bill (1) establishes specified labor protections applicable to projects funded by grants in this bill and for manufacturers of specified products; and (2) directs 40% of state, local, and tribal grant funding for grants provided by this bill to purchases that benefit frontline, disadvantaged, and vulnerable communities that have been environmentally neglected. The bill establishes within DOE a Green Procurement Oversight Advisory Board. The Government Accountability Office shall conduct oversight of the use of funds and publicly report on program efficacy each year.