Forest Conservation Easement Program Act of 2023 This bill replaces the Healthy Forests Reserve Program (HFRP) with a new forest conservation easement program. Both the HFRP and the new program provide for the Department of Agriculture (USDA) to purchase easements on private land for forest conservation purposes. Under the new program, USDA must provide cost-share assistance to states, local governments, Indian tribes, or certain organizations for their purchase of forest conservation easements. The bill also sets aside program funding to purchase easements from certain classes of landowner, including beginning forest landowners, socially disadvantaged forest landowners, and veteran forest landowners.