How can I transfer my retirement visa to a new province in Thailand?

𝟭. 𝗪𝗵𝗮𝘁 𝗱𝗼𝗲𝘀 𝗶𝘁 𝘁𝗮𝗸𝗲 𝘁𝗼 𝗺𝗼𝘃𝗲 𝘁𝗵𝗲 𝘃𝗶𝘀𝗮?. 𝗜𝘀 𝗶𝘁 𝗽𝗼𝘀𝘀𝗶𝗯𝗹𝗲?

First off I would wager you're not here on any visa 😮 The stamp in your passport most likely says "extension of stay permitted until" and has a date. <- that is NOT a visa, that's a yearly extension.

You register that YOU moved, <- go to the immigration office file a TM28 (Change of address form) and a TM30 (notification of foreigner in residence)

𝟮. 𝗜 𝗮𝗺 𝗮𝗽𝗽𝗹𝘆𝗶𝗻𝗴 𝗳𝗼𝗿 𝗮𝗻𝗼𝘁𝗵𝗲𝗿 𝟭 𝘆𝗲𝗮𝗿 𝗲𝘅𝘁𝗲𝗻𝘀𝗶𝗼𝗻 𝗯𝗲𝗳𝗼𝗿𝗲 𝗶𝘁 𝗲𝘅𝗽𝗶𝗿𝗲𝘀 𝗶𝗻 𝗠𝗮𝘆. 𝗖𝗮𝗻 𝗜 𝗱𝗼 𝗶𝘁 𝘁𝗵𝗲𝗻?

At most offices you can apply for a new extension when you have 30 days or less left on your current stamp (some offices allow you to do it when you have 45 days or less) So when you go to the immigration office in the area where you now live to file the change of address and the TM30 get the hand out from them listing the requirements for a yearly extension based on retirement so you know what that office requires

𝟯. 𝗗𝗼 𝗜 𝗻𝗲𝗲𝗱 𝘁𝗼 𝗹𝗲𝘁 𝗶𝘁 𝗲𝘅𝗽𝗶𝗿𝗲 𝗮𝗻𝗱 𝗴𝗲𝘁 𝗮𝗻𝗼𝘁𝗵𝗲𝗿 𝗼𝗻𝗲?.

Nope, you're not moving anything other than YOUR ADDRESS, and by doing that (filing a change of address and a TM30) you're registering that you are in an area served by the immigration office so you can use them for your 90 day reporting and for your next yearly extension.