Such a restrictive covenant in your contracts with students would almost certainly be unenforceable. There has to be something 'unique' in a course of instruction in order for the tutor to retain the sole right to use it.
For example, if you sign up with a weight-loss organisation, such as WW or Slimming World, they can legally prevent you from using their own ('unique') points-based systems (or similar) in any weight-loss programme which you might then go on to set up yourself. However what they most definitely can't do is to prevent you running your own weight loss classes, per se.
Anything you might write into the contracts signed by your students which seeks to prevent them going on to teach similar classes would almost certainly be regarded as an unlawful restraint of trade and therefore totally unenforceable.