Promoting Hydropower Development and Jobs Act This bill amends the Federal Power Act to authorize the Federal Energy Regulatory Commission (FERC) to establish an expedited process for issuing and amending licenses and preliminary permits for qualifying hydropower facilities that will be associated with existing nonpowered dams. In establishing the expedited process, FERC shall convene an interagency task force with federal and state agencies and Indian tribes to coordinate the regulatory process associated with the authorizations required to construct and operate a qualifying facility. FERC must assess the safety of existing nonfederal dams and other nonfederal structures related to a qualifying facility before licensing the facility. FERC must coordinate with the Department of the Army, the Department of the Interior, and the Department of Agriculture to jointly develop a list of existing nonpowered federal dams that have the greatest potential for nonfederal hydropower development. Licensees of a qualifying facility are not required to pay an annual charge for administrative expenses until construction commences.