USS Damascus
From Star Trek: Theurgy Wiki
The USS Damascus was a 24th century Federation starship operated by Starfleet.
In 2336, Lieutenant Commander Hathev of Vulcan was assigned to the Damascus where she served as the Chief Counselor for the next twenty years. Although Hathev made a point of requesting leave when the biological condition known as the pon farrwas due, in 2352 she was unable to return home and during the ritual she became pregnant from another Vulcan aboard the Damascus. She gave birth to her son on Earth, and she and Triss agreed to raise him together. For the first four years of their son's life Hathev remained aboard the Damascus, but in 2356 she applied for tenure at Starfleet Academy and the family moved to San Francisco.
(Although it has not yet been revealed what class of starship the USS Damascus was, it must have been an early mid 24th century vessel large enough to have an entire Counseling Department instead of a single ship's counselor such as such as an Ambassador, Curry, Excelsior, or Fredrickstad class.)