Postal Employee Appeal Rights Amendments Act This bill extends federal employee protections against adverse personnel actions, including the right to appeal such actions to the Merit Systems Protection Board, to additional categories of employees at the U.S. Postal Service (USPS). Specifically, it extends such protections to any officer or employee of the USPS who is not represented by a bargaining representative and is in a supervisory, professional, technical, clerical, administrative, or managerial position covered by the Executive and Administrative Schedule.