The Calypso, docked on the underside of the saucer section.
The Calypso was the captain's yacht aboard the USS Enterprise-D. (Star Trek: The Next Generation Technical Manual)
Background
The Calypso was never seen in use or mentioned in dialog, but its designation comes from the TNG Technical Manual. It was named for Jacques-Yves Cousteau's ship Calypso by Patrick Stewart. Production staff wanted to use the yacht in episodes such as TNG: "The Neutral Zone" and "Samaritan Snare", but budget restrictions prohibited building a miniature and sets. The yacht did not become part of Trek canon until the debut of the USS Enterprise-E's Cousteau in Star Trek: Insurrection.
It was likely destroyed when the saucer section of the Enterprise-D crash landed on Veridian III as it was usually docked to the underside of the saucer.
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