Building Equitable Access to Contribute to Our National Security Act of 2021 or the BEACON Act of 2021 This bill implements plans and requirements related to minority institutions of higher education and their contributions to national security efforts. Specifically, the bill requires the Department of Defense (DOD) to submit a plan for the establishment of the Minority Institute for Defense Research. The plan must be made available on a publicly accessible DOD website. DOD is authorized to establish a program to award grants to leading minority institutions to, among other purposes, advance research capabilities relating to national security. Under the bill, certain contracts awarded to educational institutions must include a requirement to subcontract with one or more minority institutions for a total amount of at least 5% of the amount awarded in the contract.