Promoting the Launch of Aviation's Next Era Act of 2021 or the PLANE Act of 2021 This bill revises provisions related to the Federal Aviation Administration (FAA), including provisions for air traffic controllers and protections for the aviation community. Among other things, the bill expands pilot protection to include that pilot facing an investigation by the FAA can appeal to a federal district court for de novo review, establishes a five-year public-private partnership for general aviation airports to attract private sector investments, designates certain general aviation airports as disaster relief airports, directs employees and staff of the FAA Academy responsible for training air traffic controllers to remain open during a government shutdown, provides practical experience for trainee air traffic control operators, and requires that all tax receipts from aviation fuel sources are deposited in the Airport and Airway Trust Fund.