Restore Everyone's Sleep Tonight Act of 2019 or the REST Act of 2019 This bill authorizes an airport to impose an access restriction between the hours of 10 p.m. and 7 a.m. for aircrafts. An airport may impose a noise deterrence penalty on an air carrier or aircraft operator for a violation of the access restriction. The restriction does not apply to the operation of military, law enforcement, and Coast Guard flights.