(covers information from several alternate timelines)
A liaison officer was a spokesperson who represented the interests of his or her government or other affiliation.
In 2370, Deanna Troi was made Ambassador Loquel's personal liaison officer for the duration of the Iyaaran's stay on USS Enterprise-D. (TNG: "Liaisons")
Kira Nerys was the Bajoran liaison officer on board the space station Deep Space 9 since 2369, representing the Bajoran Provisional Government and the Bajoran Militia when the Federation helped rebuild it. (I AM ERROR)
One job of the liaison officer aboard DS9 was to compile the material subsistence report, a job that Commander Sisko had to do when Kira was unable to assist him. (DS9: "Progress")
Julian Bashir acted as a liaison when the Federation ambassadors Taxco, Lojal, Vadosia, and Lwaxana Troi visited Deep Space 9 later in that year. (DS9: "The Forsaken")
Li Nalas was made Deep Space 9's liaison officer by Jaro Essa for a brief period in early 2370. It was shortly after his return from prison on Cardassia IV. (DS9: "The Homecoming", "The Circle", "The Siege")
A Cardassian liaison officer kept in close contact with Starfleet Admiral Kennelly during the crisis involving the Bajoran resistance leader Orta and his alleged attack on Solarion IV. (TNG: "Ensign Ro")
T'Rul served as a Romulan liaison officer assigned to supervise the operation of a cloaking device loaned to the Federation and installed on the USS Defiant in 2371. (DS9: "The Search, Part I", "The Search, Part II")
In an alternate timeline, when it took USS Voyager 23 years to return to the Alpha Quadrant, B'Elanna Torres served as a Federation liaison to Qo'noS, the Klingon homeworld in 2404. (VOY: "Endgame")