(historical) elementary school, national elementary school

school supported by a pro-North Korean organization

school supported by a pro-South Korean organization

school grammar / (specifically) Japanese school grammar, based on Shinkichi Hashimoto's work and now universally employed in Japanese schools and dictionaries.

school for special needs

military academy, (especially) the Imperial Japanese Naval Academy

driving school

(education) high school, senior high school

academy or non-university college (a post-secondary school not legally considered a university)

academy (specialized school), vocational school