Two points:
1) You don't need an ATPL at all. I would guess that most instructors only have a CPL (although most have the ATPL exams and many have an IR, and therefore have what is coloqueally called a "frozen ATPL").
2) In fact, you don't even need a CPL. You can instruct on a PPL with a Flying Instructor rating. But you need to have passed either the CPL or the ATPL written exams, and the hours requirements for getting the FI(R) rating are higher than if you do hold a CPL - see LASORS for details. A PPL instructor can not get paid for instructing, and this may raise some issues of instructors resenting the fact that you are doing their job for free.
FFF
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