I don't know any dramas that fit exactly what you've described, but I can think of a few that are somewhat close:
- Doctors - the ML and FL first meet as a teacher and high school student and their age difference prevents them from being in a relationship, but they meet again several years later as doctors when the FL is an adult
Met as Kids + ML Is a Few Years Older (Small Age Gap):
- The Smile Has Left Your Eyes - the ML and FL met as children and the ML is a few years older than the FL; the FL's adoptive brother is strongly opposed to the FL having any kind of relationship with the ML, although not because of an age gap
- What's Wrong with Secretary Kim - the FL met either the ML or the SML as a child (obviously its the ML but they try to make it seem like its the SML for a while) and he is a few years older than her
Big Age Gap But It's Not an Issue (Social Status Is) + They Did Not Meet When They Were Young:
- Mr. Sunshine
- Marriage Contract
- Love in the Moonlight
Supernatural + the ML Met the FL When She Was a Child:
- Goblin
- Hwayugi / A Korean Odyssey
- You Who Came from the Stars
