Dream Act of 2021 This bill directs the Department of Homeland Security (DHS) to cancel removal and grant lawful permanent resident status on a conditional basis to an alien who is inadmissible or deportable or is in temporary protected status who (1) has been continuously physically present in the United States for four years preceding this bill's enactment, (2) was younger than 18 years of age on the initial date of U.S. entry, (3) is not inadmissible on various grounds such as those related to crime or security, and (4) has fulfilled specified educational requirements. DHS shall cancel the removal of, and adjust to the status of an alien lawfully admitted for permanent residence on a conditional basis, an alien who was granted Deferred Action for Childhood Arrivals (DACA) status unless the alien has engaged in conduct that would make the alien ineligible for DACA. DHS shall remove the conditional basis of the permanent resident status granted under this bill if the alien meets various requirements, such as (1) maintaining residence in the United States, and (2) acquiring a degree from an institution of higher education or serving in the uniformed services. DHS may not disclose or use information provided in applications filed under this bill or in DACA requests for immigration enforcement purposes. The bill repeals a restriction barring states from providing higher education benefits to undocumented aliens unless those benefits are available to all U.S. citizens.