It is a weak, but not incorrect, sentence. As you pointed out, people will interpret it in two opposing ways. Some people, including many native speakers, will read it and think he has been a teacher for the last three years. Other people will think that he stopped being a teacher three years ago. The second interpretation is the correct one but a sentence that 50% of native speakers will misunderstand should not be spoken. It can be cleared up like this: If he started teaching three years ago, say "It is (or 'has been') three years NOW since he BECAME a teacher". If he stopped teaching three years ago, avoid the word "since" and say "He has not been teaching for three years now." or "For three years now he has not been teaching."

"He hasn't been a teacher for three years."

It means he has not been a teacher for three years. It would be clearer to say "It's been three years since he was a teacher" or "It's been three years since he last taught at school" or something like that. I hope that helps.

This type of sentence is often made clearer by emphasising the time since X happened. Like this. Making the sentence longer, long sentences are a part of the English language. Although you may be taught to make sentences shorter, In English sometimes you can't. 1. It has been three years since he was last a teacher. 2. It has been three years since he last taught. Also these type of sentences can't always be shortened, when you do so you get ambiguity of meaning.

Is it grammatically correct? Yes. Meaning: He stopped being a teacher three years ago.