The most common Korean word for “happen” is 나다 (nada). There is one more word with a similar meaning — compare them below. 「happen」는 한국어로 나다.
happen; break out; come out
TOPIK 1 · verb
to happen; to appear
TOPIK 2 · verb
Words and levels: TOPIK I essentials (National Institute of Korean Language standard curriculum, KOGL Type 1) · examples: Cheesepotato