Global Labor Support Act of 2021 This bill addresses U.S. foreign policy concerning labor rights, including in Bangladesh. Specifically, the bill authorizes visa- and asset-blocking sanctions on foreign persons responsible for gross violations of the human rights of workers. The bill also replaces the position of Special Representative for International Labor Affairs at the Department of State with the position of Ambassador-at-Large for Global Labor Rights. The ambassador must lead U.S. diplomatic engagement on labor issues. Additionally, the State Department, the U.S. Agency for International Development (USAID), and the Department of Labor must carry out activities to protect and promote labor rights worldwide; the bill establishes a fund in the Department of the Treasury for those activities. Additionally, USAID must extend through FY2028 its Global Labor Program, which supports worker organizations in addressing labor issues in their countries. The bill also requires reporting on labor issues. The State Department must annually report on the status of internationally recognized labor rights in certain countries, including any country receiving U.S. foreign assistance. If a report indicates that a country has poor performance on labor issues, Labor must deploy personnel to the U.S. mission in that country to lead interagency coordination of the labor portfolio. The Government Accountability Office must also assess U.S. government efforts concerning labor rights globally. Furthermore, the bill sets out requirements concerning labor rights in Bangladesh, such as directing the President to work with the government of Bangladesh on updating its commitments to labor rights and worker safety.