Access to Counsel Act of 2021 This bill provides various protections for covered individuals subject to secondary or deferred inspections when seeking admission into the United States. Covered individuals include U.S. nationals, lawful permanent residents, aliens in possession of a visa, returning asylees, and refugees. The Department of Homeland Security shall ensure that a covered individual subject to secondary or deferred inspection has a meaningful opportunity to consult with counsel and certain related parties, such as a relative, within an hour of the start of the secondary inspection and as necessary during the inspection process. The counsel and related party shall be allowed to advocate on behalf of the covered individual, including by providing evidence and information to the examining immigration officer. A lawful permanent resident subject to secondary or deferred inspection may not abandon lawful permanent resident status until the individual has had a meaningful opportunity to seek advice from counsel, unless the individual voluntarily and knowingly waives in writing this opportunity to seek counsel's advice.