A linguist is a person who studies linguistics. Xenolinguists focus on alien languages, and archaeolinguists study ancient or dead languages.
Thoma was a linguist assigned to the Enterprise during James T. Kirk's first five-year mission as captain ("Once More With Feeling"), while Janíce Kerasus was a linguist assigned to the Enterprise during the second five-year mission. (TOS novels: The Wounded Sky, My Enemy, My Ally, and Doctor's Orders)
Hugh Sesay was a communications specialist assigned to the USS Bluford in 2298 when that ship intercepted transmissions later found to be from a Tzenkethi Coalition ship. (Star Trek: Avenger: "Nearly a Valediction")
A chief linguistics officer was a position on some Starfleet vessels. Benjamin Caldwell was the chief linguistics officer aboard the USS Cantabrian in 2372, taking over from Threk, who was killed in a battle with the Myhr'an aboard Starbase Expanse 3 in the same year. (Star Trek: The Cantabrian Expeditions: "Catalyst, Part One")
Timothy Sinclair taught a course in linguistic studies at Starfleet Academy in 2367. He worked as an archaeolinguist with the Daystrom Institute in the late 2370s, and again in 2385. (Star Trek: Pendragon)