TPS and DED Protection Act of 2021 This bill provides a path to lawful permanent resident status for qualifying aliens who, on or before a certain date (1) had or were eligible for temporary protected status (TPS), or (2) had received deferred enforced departure (DED) status. (TPS is available to nationals of designated countries, and an alien with such status is allowed to remain in the United States with work authorization. DED status also prevents removal and provides work authorization.) A qualifying alien must have been continually present in the United States for at least three years before this bill's enactment. An alien who previously had TPS or DED status and was removed or departed solely due to the termination of such status may apply for lawful admission as a permanent resident from abroad, subject to certain conditions. Certain grounds for inadmissibility, such as an alien likely being a public charge, shall not apply to aliens applying for permanent resident status under this bill. The parents, spouse, or unmarried child of an alien admitted for permanent residence under this bill shall also be admitted for permanent residence. Qualifying aliens admitted for permanent residence under this bill shall be eligible for naturalization. Language proficiency requirements related to naturalization shall be waived for such aliens. Venezuela and Eritrea shall be treated as designated TPS countries. Within three days after announcing the termination a country's designation for TPS, the Department of Justice shall report to Congress the circumstances surrounding the termination.