What is the ruling on female teachers giving a gift to their principal to express their gratitude and appreciation, while they will remain under her administration for the coming year, and does this fall under the ruling on gifts to employees?

It is not permissible for an employee to give a gift to his manager as long as the professional relationship between them exists, because this falls under the category of gifts to workers, which are considered 'ghulul' (embezzlement/misappropriation) and are forbidden. The Prophet, peace and blessings be upon him, prohibited this due to the fear of bias and bribery, even if the employee works under the supervision of this manager.