cram school teacher
Refers to a teacher at a 塾 (juku), a private after-school tutoring or exam-preparation academy. The term is neutral and widely understood.
He teaches mathematics as a cram school teacher.
I'm looking for a part-time job as a cram school teacher.
Compound of 塾 (juku, 'cram school') and 講師 (kōshi, 'lecturer/instructor'). The exact historical derivation is straightforward from the component meanings.