Z visa and a new employer

Hello. My husband and me, both work here in China on Z which has been granted by our current employer. However our contract completes on 15th August, but our resident permit is valid till November. We don't plan to extend the contract and stay with the same school. The question is what will happen with our resident permit and Foreign Expert Certificate when we change the employer. Do we have to make an exit to HK and get a new Z there or we should go back to our home country and start the procedure from the beginning. Thanks