Stop Higher Education Espionage and Theft Act of 2021 This bill establishes a process for designating foreign actors as foreign intelligence threats to higher education. Specifically, the Federal Bureau of Investigation (FBI) must designate a foreign actor as a foreign intelligence threat to higher education if the foreign actor has committed, attempted to commit, or conspired to commit certain actions in connection with an institution of higher education (IHE), such as espionage, misuse of visas, or theft of trade secrets. Prior to making such a designation, the FBI must submit notice to Congress and the Department of Justice. Upon the designation of a foreign actor as a threat, the Department of State must revoke the nonimmigrant visa issued to the foreign actor present in the United States, and the Department of Homeland Security must initiate removal proceedings against the foreign actor. Additionally, the bill provides for judicial review and a process for revoking a foreign actor's designation as a threat. Finally, the bill also requires an IHE to disclose to the Department of Education any gift or contract with a foreign intelligence threat, including the fair market value of the gift or contract.