Teachers Leading, Educating, Advancing, and Designing Act of 2023 or the Teachers LEAD Act of 2023 This bill directs the Department of Education (ED) to (1) award competitive grants to eligible entities (e.g., local educational agencies) to carry out teacher leadership programs, and (2) coordinate with the Department of the Interior to develop and implement a teacher leadership program plan for and award grants to Bureau of Indian Education schools. Further, ED may award planning grants to eligible entities to develop program proposals. The Institute of Education Sciences must conduct an independent evaluation of grant activities.