Assuring Private Property Rights Over Vast Access to Land Act or the APPROVAL Act This bill amends the Energy Policy Act of 2005 to prohibit the Department of Energy and the Southwestern and Western Area Power Administrations from using the power of eminent domain to implement modernization of electricity transmission infrastructure, unless they have received explicit permission to do so by: (1) the state governor and the head of each applicable public utility commission or public service commission of the affected state, and (2) the head of the governing body of each Indian tribe whose land would be affected. An electricity transmission infrastructure project, to the greatest extent practicable, must be sited upon either an existing federal right-of-way or upon federal land managed by either: (1) the Bureau of Land Management, (2) the Forest Service, (3) the Bureau of Reclamation, or (4) the U.S. Army Corps of Engineers.