National Center for the Advancement of Aviation Act of 2023 This bill establishes the National Center for the Advancement of Aviation to (1) develop a skilled and robust U.S. aviation and aerospace workforce; (2) serve as a national independent forum to support collaboration and cooperation between governmental, nongovernmental, and aviation and aerospace industry stakeholders regarding the advancement of the U.S. aviation and aerospace workforce; and (3) serve as a repository for research conducted by institutions of higher education, research institutions, or other stakeholders regarding the aviation and aerospace workforce, or related technical and skill development. The center must perform the following duties improve access to aviation and aerospace education and related skills training to help grow the U.S. aviation and aerospace workforce; support Armed Forces personnel and veterans seeking to transition to a career in civil aviation or an aerospace-related field through outreach, training, apprenticeships, or other means; and amplify and support the research and development efforts conducted as part of the National Aviation Research Plan and work done at the Federal Aviation Administration Centers of Excellence and Technical Centers regarding the aviation and aerospace workforce. Additionally, the center may issue grants to certain entities to, among other things, (1) establish new education programs that teach technical skills used in aviation maintenance; (2) establish scholarships, internships, or apprenticeships for individuals pursuing employment in the aviation maintenance industry; and (3) support outreach about educational opportunities and careers in the aviation maintenance industry.