A fiancé, in Human society, was a person who was engaged to be married to another.
In 1947, Faith Garland's mother suggested that she and her fiancé, Jeff Carlson went to Niagara Falls for their honeymoon. (DS9: "Little Green Men")
Doctor Roger Korby was once engaged to Nurse Christine Chapel. (TOS: "What Are Little Girls Made Of?")
In 2266, Angela Martine was about to marry her fiancé, Robert Tomlinson. The wedding was postponed when the USS Enterprise became involved in a battle with a Romulan Bird-of-Prey, during which Tomlinson inhaled toxic levels of Phaser coolant and later died. (TOS: "Balance of Terror")
In 2370, Nurse Alyssa Ogawa became engaged to Lieutenant Andrew Powell on the USS Enterprise-D. Soon after, she became pregnant with their first child. (TNG: "Lower Decks", "Genesis")
Captain Kathryn Janeway's fiancé was Mark Johnson, whom she last spoke to just before the USS Voyager was lost in the Delta Quadrant. Johnson held onto the hope that the starship and its crew were still alive, but eventually married someone else. (VOY: "Caretaker", "Hunters")
Counselor Deanna Troi and Commander William T. Riker were fiancés at one point, eventually marrying in 2379. (Star Trek Nemesis)