Maintaining and Enhancing Hydroelectricity and River Restoration Act of 2023 This bill establishes a new investment tax credit in the amount of 30% of the basis of any hydropower improvement property. The bill defines hydropower improvement property as property that adds or improves fish passage at a qualified dam; maintains or improves the quality of the water retained or released by a qualified dam; promotes downstream sediment transport and habitat maintenance; upgrades, repairs, or reconstructs a qualified dam to meet safety and security standards; improves public uses of, and access to, public waterways impacted by a qualified dam; removes an obsolete river obstruction; or places into service an approved remote dam. Further, written approval for hydropower improvement property must be obtained from the Federal Energy Regulatory Commission or state or local officials prior to January 1, 2032. The bill also allows an election to claim the investment tax credit for qualified progress expenses for some types of hydropower improvement property in advance of such property being placed into service. Any investment tax credit amount claimed for qualified progress expenses reduces the amount of the investment tax credit that may be claimed once the hydropower improvement property is placed into service. The bill authorizes certain entities, including tax-exempt and governmental entities, to treat the investment tax credit for hydropower improvement property as a payment of tax and receive a refund of any overpayment (also known as elective pay). Finally, the investment tax credit for hydropower improvement property may be transferred (i.e., sold).