Green Spaces, Green Vehicles Act of 2021 This bill directs the Department of Energy (DOE), the Forest Service, and the National Park Service (NPS) to collaborate on a Green Spaces, Green Vehicles Initiative to facilitate the installation and use of zero-emissions vehicle infrastructure, including on land that is not National Forest System land or NPS land. The agencies shall facilitate such installation and use, including by acquiring zero-emissions vehicles for the fleets of the Forest Service and the NPS. For purposes of determining whether the acquisition of alternative fueled vehicles is practical for the fleet of the Forest Service or the NPS, DOE shall take into account the availability on National Forest System land or NPS land, as applicable, of zero-emissions vehicle infrastructure.