If your visa has expired or you did not get a re-entry permit then you can come on a Visa exempt stamp and change it to a Non-O visa whilst you are here if you can fulfil the same conditions as your previous Non-O visa.
First thing first. No car or motorcycle has a license that's for the driver or rider. I know there are many of these in Thailand but hoq many legal!!. yours seems to have got tax with the chair attached. Many people have told me (as others on here agree), that they are not actually legal. I don't have one so can't be sure but do note that are not mentioned on Thai driving licences.