I'm not sure if it's legal to actually teach without a license/degree in Korea, but you're asking if you can do it privately. Millions of college students today tutor high school/junior high students privately to support their way through school. I'm not sure if it's legal or not, but I highly doubt you'll get prosecuted for it. In fact, many Americans/Canadians go to Korea to teach/tutor and they do not have a degree. They even have programs where any college student regardless of their major, can go to Korea to teach English. I hope this answers your question. Foreign people willing to teach their native language is highly in demand, with or without their degree.