A small Starfleet vessel on which Data served before joining the Enterprise-D, mentioned in 2364 as too slow to help at Starbase 74 and in 2367 for an encounter with a wormhole.
The USS Trieste is mentioned in two Next Generation episodes. In 11001001, when the Bynars steal the Enterprise from Starbase 74, the only other Starfleet ship in the area is the Trieste, which is dismissed as too small and too slow to give chase.
In Clues, after the crew apparently lose consciousness while passing through what seems to be an unstable wormhole, Picard recalls that Data was aboard the Trieste when it went through a similar phenomenon, and Data uses that experience in explaining what should have happened.
The ship is never seen. The two references together establish it as one of Data's assignments in the years between his graduation from Starfleet Academy and his posting to the Enterprise.