The Triple Over is the personal flagship of Orion Syndicate leader Ard Jarikar.

In 2387, a Starfleet pirate-hunting fleet led by Admiral Mitchell and the USS Potemkin chased the Triple Over into the caverns beneath the smuggler's planet of Targ's Arse. (TEM: "Indistinguishable from Magic, Part I")

Later in that same operation, the Potemkin crew stole the Triple Over, both as a way to gain intelligence on the Orion pirate and, as Commander Bom said, "to piss him off." (TEM: "Indistinguishable from Magic, Part III")

A "Triple Over" is a particularly high-scoring Dabo result, and thus the nship's name is likely inspired by Jarikar's gambling interests.