Diplomatic Support and Security Act of 2021 This bill makes changes to procedures for investigating serious security incidents related to a U.S. government mission abroad. A serious security incident involves (1) the loss of life, serious injury, or significant destruction of U.S. government property abroad; or (2) a serious breach of security involving intelligence activities of a foreign government directed at a U.S. government mission abroad. Currently, accountability review boards convened by the Department of State investigate and report on these incidents. Under this bill, the State Department Diplomatic Security Service must assemble a team to investigate a serious security incident. An assembled team must prepare a report about the incident under investigation that (1) details relevant facts and circumstances; (2) accurately accounts for the casualties, injuries, and other damage; and (3) assesses applicable security procedures and countermeasures. After the investigation, the State Department must convene a coordinating committee to review the investigation report and make findings about, for example, the adequacy of security measures and the impact of intelligence and information availability. Members of the committee must be Assistant Secretary-level officials at the State Department, including the Assistant Secretary for Diplomatic Security, the Assistant Secretary responsible for the region where the incident occurred, and other designated officials. The committee must provide, within 30 days, its findings and related recommendations to the Secretary of State. The findings and related recommendations must also be shared with Congress.