Can you leave school and start an apprentiship at 16 and return to do your exams?

Maybe. It depends on where you live, and what kind of apprenticeship program.

Many high schools offer trade programs, where students can begin this kind of training while still enrolled. If so, you will be permitted to do so. If not, it depends. If the age of compulsory attendance is 16 or below, you can leave school without being truant. If the age is 17 or 18, you cannot drop out until that age. If you are in an area where you are permitted to drop out at 16, it then depends on whether or not the school will allow you to re-enroll in the same term.