If my employee converts from full time to part-time employment, do I need to terminate his current contract and issue him a new contract? Would his employment be considered continuous?

If your employee converts to part-time without a break in service, his employment is considered continuous. Any changes to the terms of the original contract must be in writing. To prevent misunderstandings or disputes, you should issue a new contract with the terms and conditions of part-time employment, signed by you and your employee.