Many people coming to the end of their teaching contracts this month and next who get a new job, can they transfer new employer onto their work permit and continue to stay in the country without their visa being cancelled. Probably been answered before but I can't find.

Visas are not cancelled. Only an extension of stay issued by immigration can be cancelled.

A work permit cannot be transferred to a new employer.

It is possible to change employers without leaving the country but it cannot be done without leaving the current job by doing it properly by giving notice to them.

The new employer would need to apply for the new work permit needed and obtain a work permit application approval letter. Then with paperwork from the new employer and the approval letter a new extension can be applied for after the current extension of stay is canceled by presenting a termination letter from the current employer dated for the date the application is done. Then the existing work permit would be cancelled and the new one issued.