Is it permissible for a teacher who left an online school due to a dispute with the administration to teach former students, or their relatives, or individuals referred by these students, given that the previous employment contract prohibited direct communication with students or teaching them outside the school's framework?

If the school stipulated to the teacher that he should not give his personal information to students or teach them outside of school, and he accepted the condition, then he is obliged to fulfill it, due to the Almighty’s saying: (O you who have believed, fulfill [all] contracts) and the Prophet’s (peace and blessings be upon him) saying: (Muslims are bound by their conditions).

Thus, you erred by violating the condition and giving your personal information to the students.

As for teaching those who requested it from you after you left the school, and you did not seek to teach them while your contract was active, there is no harm upon you in teaching them. It is preferable that you refrain from teaching those to whom you gave your number while you were working at the school, as a rectification of your error.