Your student info/client list is yours. SO, are your teaching methods, studio methods etc. You can have an "agreement" stating that none of this info is taken if a teacher leaves. I have a contract that I use and all of my teachers willingly signed it- except for one I didn't hire b/c she spilled the beans when it came time to sign the form that she wanted to open a studio. You have to cover your back......
by the way, I consulted my lawyer. He did not say anything about it not standing up in court. You cannot prevent someone from teaching elsewhere, but you can prevent them from opening within a certain distance within a certain time if they sign the contract.