Promote Accountability and Government Efficiency Act This bill revises the status and rights of federal civil service employees. Specifically, the bill: provides that employees hired one year after the enactment of this bill shall be hired on an at-will basis (i.e., removal or suspension for good cause, bad cause, or no cause at all); allows the suspension of such employees for misconduct or poor performance; denies a pay increase to employees who do not achieve a certain performance rating; denies a retirement annuity to an employee convicted of a felony; permits the transfer of a Senior Executive Service employee to a position in the General Schedule; and prohibits an employee from carrying out the business of a labor organization unless such employee is in a non-duty status or from using any government property in carrying out union business.