So I expect to get my replacement passport sometime this week. My current extension of stay is valid until the end of June. At that time I will need to leave Thailand.
Do I need to get my current stamp moved to my new passport if all I am going to do is leave. I have the old stamp in the old passport.
TLDR : Answer Summary
When leaving Thailand with a replacement passport, you do not need to transfer your visa stamp. It is sufficient to present both your old passport, which contains the visa stamp, and your new passport to the immigration officials when you exit.