What should I do with my visa in my old passport after receiving a new passport in Thailand?

When you receive a new passport, it's important to handle your existing visa correctly. According to comments from the community, while you can't transfer a visa, you can keep both your old passport (with the visa) and your new passport. You should carry both until your existing visa expires, after which you can apply for a new visa or extension. This approach is generally acceptable, and immigration offices are seen as helpful in these matters.