Taiwan Relations Reinforcement Act of 2021 This bill contains provisions pertaining to the U.S.-Taiwan relationship. The director of the American Institute in Taiwan's Taipei office shall be subject to the advice and consent of the Senate. (In 1979, the United States established diplomatic relations with China and ended formal diplomatic ties with Taiwan. The American Institute in Taiwan is a private organization that represents U.S. interests in Taiwan and provides consular services.) U.S. government departments and agencies (1) may not formally or informally recognize China's claims of sovereignty over Taiwan without the assent of Taiwan's people, as expressed through the democratic process; (2) shall treat Taiwan's elected government as the legitimate representative of Taiwan's people; and (3) shall end the practice of referring to Taiwan's government as authorities. The Department of State shall establish the U.S.-Taiwan Cultural Exchange Foundation, which shall work with schools to send U.S. high school and university students to Taiwan to study the Chinese language, politics, and other subjects. In addition, the State Department shall develop and implement a strategy to respond to Chinese government attempts to use misinformation, media manipulation, economic coercion, and other strategies against Taiwan or persons in Taiwan. The bill also directs the President to establish an interagency Taiwan policy task force, which shall annually report to Congress a plan for enhancing U.S.-Taiwan relations.