Expried Existing Z visa holder wants to get work permit from new company

Sameer, I don't think you can get a new one if you don't cancel your old one. In order to cancel you old one, you should ask help from your previous employer. Your employer should provide a report that includes your nationality, name, passport number and position. Also they should give you Termination of Contract Certificate. The official stamp and your signature are required. Then you can take these two pieces of documents together with your old work permit to do cancellation at local labor bureau.

If you don't want to cancel your old one, you should change your work permit with the help of your current employer. I think your current employer should do their best to assist you. The required documents are:
1.Invitation letter from your current employer. It should include why you are recruited, your position, working duration and the official stamp.
2.Employment separation certificate from your previous employer. It should state why and when you leave.
3.Your current employer’s business license and organization code certificate
4.Your work permit, passport and visa
5.Your resume
6.Your temporary residence permit
7.Your employment registration form
8.5 recent passport photos

These are basic required documents. If your employer recruited foreigners before, they should know the exact process.