Trillya was an alien Starfleet officer who served during the late 23rd century. In 2286, she served aboard the USS Shepard as a communications officer.
That year, the Shepard was among the starships disabled by the Whale Probe when Trillya sent a distress call to Starfleet Headquarters. (Star Trek IV: The Voyage Home)
Trillya was played by Jane Wiedlin, rhythm guitarist and songwriter for the rock band The Go-Go's. Her name is from the script.
The fact that she is an "alien" is taken from the film's credits, where she was as "Alien Communications Officer".
Based on the shape of her rank insignia, she was either a lieutenant junior grade or lieutenant.