The first one means, that besides a lot of other things he is also a teacher. The second one means that a lot of people are teachers and he is too. So they are both correct but the meaning is different. Mijn excuses voor mijn belabberde Engels maar ik hoop dat je het verschil in betekenis begrijpt.

Thanks, your explanation is very clear!

Yes correct! If you want to refer to "he" being a teacher, besides doing/being something else, you need to invert the verb and subject and say "Ook is hij (een) docent". The second version that you wrote, "Ook hij is een docent", you use to express that "hij", just like someone else you probably just mentioned in the conversation, is a teacher.