Teachers Empowered Against Classroom Harm Act of 2023 or the TEACH Act of 2023 This bill addresses school safety and security, including by expanding access to firearms for certain individuals and providing grants for defensive training programs. Current law prohibits the use of federal elementary and secondary education funds to provide any person with a dangerous weapon or training in the use of a dangerous weapon. The bill removes this prohibition. Next, the bill broadens the authority for certain individuals to carry firearms in a school zone. Specifically, the bill exempts individuals authorized by state law to carry firearms from the federal prohibition on possessing a firearm in a school zone. Further, the bill prohibits the Department of Education (ED) from disbursing or obligating funds for states, local governments, or eligible entities (e.g., local educational agencies or private schools) that restrict (in excess of federal law) the possession of firearms within school zones. Additionally, the bill directs ED to obligate certain reserved funds (i.e., funds reserved for technical assistance and capacity building) for a grant program. In particular, ED must award grants to enable eligible entities (e.g., local educational agencies or private schools) to participate in defensive training programs designed to protect schools from armed intruders. ED must fully obligate these funds for awarding grants and failure to do so shall result in a hiring freeze for ED.