Elected Official Lobbying Prohibition Act of 2021 This bill prohibits state and local elected officials from lobbying the federal government on behalf of private (i.e., nongovernmental) clients. The bill's restrictions apply to officials who serve in a statewide elected office, a state legislature, an elected office of a local government that meets specified population standards, or as the chair of a political party of a state, including officials of U.S. territories and the District of Columbia. The bill does not apply to officials acting on behalf of their constituents or who are otherwise acting in an official capacity.