A pirate was a person who stole valuable possessions from others aboard a starship or another type of vessel. The act itself was called piracy.
When this person acted on a sovereign government's behalf or bequest, he or she was known as a privateer. The act itself was called privateering.
The Breen were known to support privateers, with the battle between Breen privateers and the USS Shabonee in 2369 leading to the Shabonee's destruction. (Star Trek: Shabonee: "Scream") The wanted Ubessian criminal Yaghim Thau also joined forces with Breen privateers against the USS Prospect-A in 2371, with the privateers and Thau failing and being taken into custody. (Star Trek: The Prospect Chronicles: "Ramifications")