Can you register with a GP in Thailand for long-term prescriptions?

You just go to the pharmacy you don’t need a prescription order from Medisafe they deliver and there the cheapest

The concept of registering on the panel of a General Practitioner (Family Doctors) surgery or group practice as in United Kingdom doesn’t exist in Thailand. When locals want to consult a GP they go to their local community Government (National Health Service) hospital. There is usually one GP on duty. They take a turn ticket and often wait all day. However, they (or you) will be seen that day. The GP will diagnose, prescribe and dispense medications from the hospital pharmacy. The cost is very low. There have been reports of expats being able to obtain medicines at Thai Government Hospitals for less than the pharmacies charge.

No real concept of a primary care GP here although some choose to use a regular clinic in their location. As for prescriptions there is no long term plan such as in the UK where you can pay a single amount to cover all. You will jist have to find the cheapest pharmacy and buy from them. Many long time Expats here use Medisafe. You can find them online and message them. They will give you the price and may offer cheaper generics for the same meds.

It's called walking into a clinic and making an appointment. Then remembering that clinic and going again.

What do you mean by "register"?