Global Health Security Act of 2021 This bill directs the United States to implement a strategy to strengthen global health security, including by requiring the President to create the Global Health Security Agenda Interagency Review Council to implement the Global Health Security Agenda. The agenda is an initiative launched by nearly 30 nations to address global infectious disease threats. The council's responsibilities include (1) providing policy recommendations on agenda-related goals, objectives, implementation, and other international efforts to strengthen pandemic preparedness and response; (2) helping federal agencies with implementation; and (3) reviewing the progress and challenges in achieving U.S. commitments, including assistance to help other countries meet agenda targets. The bill also directs the federal agencies involved with the agenda to prioritize its implementation and to take certain steps to achieve that goal. The President shall coordinate a strategy for responding to global health security emergencies and submit a report on the implementation of this strategy. Additionally, the Department of State should seek to enter into negotiations with donors, relevant United Nations agencies, and other multilateral stakeholders to establish a Fund for Global Health Security and Pandemic Preparedness that (1) closes gaps in global health security and pandemic preparedness; and (2) builds capacity in eligible partner countries related to global health security, infectious disease control, and pandemic preparedness. The fund should provide grants, technical assistance, and innovative funding mechanisms to achieve its purposes.