If a foreigner leaves a job for whatever reason, they need to hand back the work permit to the labor department and the visa that goes with that work permit becomes invalid. You then have to leave the country to obtain a new visa at a Thai embassy or consulate in the neighboring countries.
Once in Thailand the work permit application shall follow. Note that if you want to add another job such as a part-time job to an existing work permit then you need to speak to an attorney about having it added onto your current work permit.
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