A liaison was an individual who acted as an intermediary between two parties. This person could be officially designated as a liaison officer.
When Bajor was under Cardassian occupation, Secretary Kubus Oak was the special liaison between the Cardassian Union and the Bajoran Occupational Government, living onboard Terok Nor before relocating to live on Cardassia Prime. However, in reality, Kubus was a collaborator that maintained the appearance of cooperation between the occupying force and their pawns within the puppet administration. (DS9: "The Collaborator")
In 2267, Governor Kor appointed "Baroner" (who had been described as a leading citizen of the Organians) as a liaison between the occupying forces (the Klingons) and the civil population (the Organians). (TOS: "Errand of Mercy")
In 2268 while recording an entry in the ship's log, Hikaru Sulu described Ensign Pavel Chekov as the liaison between Captain James T. Kirk and the USS Enterprise. (TOS: "Spock's Brain")
In 2366, Captain Rachel Garrett made Lieutenant Richard Castillo the liaison between the USS Enterprise-C and the USS Enterprise-D. (TNG: "Yesterday's Enterprise")
In 2367, Hayne demanded to Jean-Luc Picard that Ishara Yar be their liaison between the Enterprise-D and his Coalition. (TNG: "Legacy")