Refers to a person one has known for a long time, often with a sense of familiarity and trust. Slightly formal/literary tone.
He is an old friend of mine.
旧知の間柄だから、遠慮はいらない。
Since we're old acquaintances, there's no need to stand on ceremony.
He and I are old acquaintances.
When in trouble, all you can do is rely on an old acquaintance.