A diplomatic mission was a campaign with the goal of strengthening diplomatic ties with another people group.
In 2268, James T. Kirk noted in his captain's log that "on a top secret diplomatic mission, the Enterprise has entered the Tellun star system. Maintaining communications blackout, we have taken aboard Petri, Ambassador from Troyius, the outer planet, and are now approaching the inner planet, Elas." (TOS: "Elaan of Troyius")