Procedure to be followed while changing visa to another employer

My husband is under my visa (wife's visa). He found a job and the company is going to give him an employment visa.

Does he need to cancel his current visa in order to proceed for the company’s visa or just do the labour permit and give the No Objection letter?

And if he really needs to cancel his current visa, does it affect also his medical insurance or he can still continue using it even if his visa is will be under the company’s visa?

Thank you so much.