This forum is really intended for teachers of English as a foreign language. I have no experience of teaching drama. I wouldn't like to give you ideas or advice that turn out to be wrong.
All I can suggest is that you contact the Japanese consulate or embassy in your country of residence. They might have names of drama schools. You can also check Japanese websites e.g. Ministry of Education, Ministry of Culture, their equivalent of directory enquiries / yellow pages. Get the names and addresses of schools that teach drama and get in touch with them. Even if this doesn't turn out to be fruitful, they might be able to give you names of schools who hire people like you.
Whatever happens, good luck and enjoy this career move.
The information provided in this forum is intended for guidance only. We can only provide general information as situations vary from country to country. It should also be noted that economic and political situations change. We advise you to contact embassies and consulates before making decisions involving a move to another country. Tefl.net cannot be held responsible for any decisions you make based on the information provided here. It is your responsibility to gather information about employers before accepting a job.