This page contains information regarding Star Trek: Lower Decks, and thus may contain spoilers.
Second contact was deemed to be of at least some importance, as it allowed the facilitation of continued communication and ensured that all administrative documentation was complete and correct, as well as allow the visiting representatives to familiarize themselves with a homeworld that may not have been visited during first contact.
The USS Cerritos specialized in second contact missions. In 2380, they oversaw second contact proceedings with the Galardonian High Council following the first contact mission with the USS Quito the year before. (LD: "Second Contact")
The following year, the Cerritos undertook a second contact mission to Apergos, which endured unforeseen complications when Commander Jack Ransom gained god-like powers after being imbued with strange energies. (LD: "Strange Energies")