Hong Kong People's Freedom and Choice Act of 2021 This bill provides for temporary protected status (TPS) for qualifying Hong Kong residents and contains other immigration-related provisions. Hong Kong shall be treated as a TPS-designated territory for 18 months starting from this bill's enactment. (Qualifying nationals of a TPS-designated territory or country may not be removed from the United States and shall have employment authorization while the designation is in effect.) Furthermore, Hong Kong shall be treated as separate from China for the purposes of various numerical limitations on immigrant visas. (In the treaty that transferred sovereignty of Hong Kong to China, China pledged that Hong Kong "will enjoy a high degree of autonomy.") The bill also establishes Priority Hong Kong Resident status for qualified individuals. To obtain such status, an individual must meet certain requirements, such as having resided in Hong Kong for at least ten years as of the day of this bill's enactment and not having citizenship in any jurisdiction other than China, Hong Kong, or Macau. For seeking refugee status or asylum, a Priority Hong Kong Resident may establish a well-founded fear of persecution based on various factors, such as fear based on the individual's significant role in certain protests against China's encroachment into Hong Kong's autonomy. The Department of Homeland Security (DHS) or the Department of State may provide special immigrant status to an eligible Priority Hong Kong Resident with a bachelor's or graduate degree if DHS determines that doing so would provide a significant benefit to the United States.