The eligible visa types to work in Korea are short-term employment (C-4), university professor (E-1), foreign language/conversation instructor (E-2), research (E-3), technology transfer (E-4), professional employment (E-5), arts & performances (E-6), special occupation(E-7), nonprofessional employment (E-9), vessel crew (E-10), and working visit (H-2) .

For more details, see https://english.seoul.go.kr/service/working/employment/1-scope-of-activities-and-employment-for-foreigners-in-korea/.