Neighborhood Tree Act of 2023 This bill provides for additional assistance to states, Indian tribes, units of local government, approved organizations, and local community tree volunteer groups to plant and maintain trees. The Department of Agriculture (USDA) shall establish a Neighborhood Tree Fund from which to provide assistance to such entities to increase and improve the overall health of the tree canopies in their communities. In providing the assistance, USDA must give priority to those entities with proposed projects that include and prioritize tree planting and tree maintenance in underserved communities and neighborhoods, including those that are low-income or have a lower tree canopy. The bill modifies the composition of the membership of the Forestry Advisory Council by (1) increasing the number of council members to 16, and (2) including as a member of the council one individual who is the resident of a low-income community.