As your question is specific to ST:TNG and the Enterprise D, the following taken from https://memory-alpha.fandom.com/wiki/Captain's_yacht answers your question in full.
Designer Andrew Probert came up with the concept of the captain's
yacht while designing the USS Enterprise-D.
Although it was never seen
in use, it was labeled on the master systems display screen in main
engineering and on Commander William Riker's bridge console ("New
Ground"), docked at the bottom of the saucer section almost directly
opposite the main bridge.
Probert suggested possible ways for the
yacht to be used during the first season, including not showing the
yacht but mentioning it in dialogue, but his ideas were rejected. The
Star Trek: The Next Generation Technical Manual (p. 164) claims that
the producers almost used the yacht in TNG: "Samaritan Snare", but
decided to use an "executive shuttlecraft" due to budgetary
According to Patrick Stewart, the yacht would have been
called Calypso. (Star Trek: The Next Generation Technical Manual, p.
We didn't get to see a Captain's yacht in action until Star Trek: Insurrection
The yacht can be seen in this compilation of Enterprise E shots at ~0:55.