It depends on the kind of visa you have at the moment. If you entered China on a Z visa and your residence permit is still valid, your recruiter (school) might be able to negotiate with your current employer without you having to leave China. Your current employer will decide whether or not you will remain affiliated to them on your residence permit. If they choose to switch you over to an L visa at your expense, you’ll need to make a visa run to Hong Kong to apply for a new Z visa.