HMS Calypso was a frigate under the command of Captain Hammond when Hornblower sat his examination for lieutenant in Gibraltar. The Board of Examination consisted of Captains Foster of HMS Dreadnaught, Hammond, and Harvey of the dockyard.
During the fire ship attack the three captains and Hornblower ended up together on a wherry. Since Dreadnaught was a frigate, due to the name, and Hammond was senior to Foster, it seems that Calypso was also a frigate.
The historical Calypso was an Echo class ship-sloop launched on 27 September 1783 and sunk on 30 July 1803 during a storm due to a collision with a West Indiaman.
- Mr. Midshipman Hornblower: The Examination for Lieutenant
- HMS Calypso (1783) in Wikipedia