고 만나다

meet up after doing that

The -고 clause is what came before the meeting, or what made it possible: 이거 끝나고 만나러 가시는 줄 알고 "I thought you were off to meet him after this", 안심하고 만날 수 있었을 것 같아 "I think I could have met them without worrying". Two lines show how a Korean get-together actually gets arranged: "시간 되면 밥 한 번 먹어요" 하고 만난 친구, and 우리 얼굴 한번 보자 해가지고 만나는 게 송년회 — that vague "let's grab a meal sometime" turning into a real meeting.