International Press Freedom Act of 2021 This bill establishes programs to address international threats to press freedom and allows qualifying threatened journalists to be admitted into the United States. The bill establishes an Office on International Press Freedom within the Department of State. The office's duties shall include (1) advocating for freedom of the press and freedom of expression abroad, (2) advising on U.S. policy on advancing such freedoms abroad, and (3) representing the United States in matters relating to such freedoms. The bill also establishes the At-Risk Journalists Fund. The State Department shall use the fund to support journalists operating in restrictive environments and provide emergency assistance to journalists who have been threatened. If the assistance provided through the fund is insufficient to protect the safety of an alien journalist who has been threatened, the journalist may receive a foreign media nonimmigrant visa upon meeting certain qualifications. The State Department must prioritize the review of a visa application for such a threatened journalist. Similarly, the Department of Homeland Security must consider providing humanitarian parole to threatened journalists and provide an admission preference to certain threatened journalists (generally if the journalist's life or safety is at risk and if paroling the journalist would further U.S. foreign policy or national security interests). The Department of Justice must provide training to all officials adjudicating refugee cases about issues involving freedom of the press. The State Department must also provide training on such issues to certain Foreign Service officers working overseas.