Teacher specific transferring employer

[MissSB]

I am employed on a 3 year sponsored visa, currently in my 2nd year. I believe that the sponsorship is through the borough council, working at a state school.
1) Am I able to transfer to another state school within the same borough without starting a new sponsorship application process?
2) If I were to move into the private sector, would I have to start the sponsorship application process again, after finding a school to sponsor me?
3) Does it cost the school/council an additonal anount should I transfer schools within the same borough?
Any help would be appreciated.