Transferring to another sponsor company?

Im currently working here in riyadh for 2 years under a specific employer. I was renewed by my hospital company without my knowledge but now i decided and applied to another employer.

The new employer wants me to do a local transfer since the hospital im applying is still located in ksa and they want to do a local transfer.

As far as i know my hospital does not approve of local transfer. They will issua an exit instead....

Does anyone know how to process this local transfer? Thanks.