Is it permissible for a female teacher to leave three hours before the start of the school day during the return-to-school period, with the knowledge and approval of the administration, given that she has no work to do?

If the school administration permits female teachers to leave due to a lack of work, there is no harm in that; because the administration is authorized to assess the interest of the work. According to Sheikh Ibn Baz, it is not permissible for an employee to leave their work before the end of working hours except with permission from a responsible authority.