Caption: The Captain's yacht
Caption: The Cousteau disembarks and docks under the saucer section
Caption: Captain's Yacht
Apparently a newer Starfleet tradition, this large, elliptical, shuttle vehicle appeared on Galaxy-class starships. The Captain's yacht docks and disembarks from an external port located on the underside of the saucer module.
The craft is intended for diplomatic missions, such as the transportation of dignitaries and ambassadors. The yacht aboard the U.S.S. Enterprise NCC 1701-D was named Calypso, in honor of a 20th-century Earth exploration vessel, commanded by Captain Jaques-Yves Cousteau.