Have Work Permit - Switching Companies

New Company should apply for a new one, Company Sponsor will be different already.

This is hearsay but it came from my lawyer.  When you apply for the new WP you can reference the old permit and you will not have to provide new copies of your diploma and TEFL certificate.   Not as sure about the police check.  You may have to get a local one.  The new company will have to provide your new employment contract as well as make the application.

Did you keep a photocopy of the first WP for yourself?  You will need it if only to get the numbers to reference.  I expect the company has the original.  Obtaining new copies from them could get testy, depending on your relationship when you left.