Spaceflight Training and Astronaut Reform Act or the STAR Act This bill includes space support vehicles and training among the vehicles and purposes, respectively, for which the Department of Transportation (DOT) may establish safety approval procedures relating to an experimental permit for conducting commercial space launch or reentry activities. A "space support vehicle" is defined as an aircraft operating at a spaceport licensed by the Federal Aviation Administration that simulates space flight conditions in support of training for space flight participants or crew or testing of space flight hardware. The bill expands the vehicles for which DOT may issue an experimental permit to include reusable suborbital rockets, reusable launch vehicles, or space support vehicles, that will be launched into a suborbital trajectory, reentered, or flown for training or research purposes, including to simulate launch, reentry, or space flight conditions. The bill prohibits a space support vehicle from operating under a permit issued pursuant to this bill unless it has a valid letter of deviation authority. DOT shall issue such letter within 60 days after the permit is provided, to the extent consistent with maintaining health and safety.