Esperanza

The Esperanza was the Corsair's TARDIS which outwarldy resembled a pirate ship.

Like the Doctor, the Corsair saw their TARDIS as the best ship ever, even if the Type 60 model lacked the refinements of other TARDISes. (PROSE: One Virtue, and a Thousand Crimes) While prefering to travel alone, the Corsair did often travel with a cat and, at other times, a parrot. (PROSE: Eleven Things You Probably Didn't Know About the Corsair)

History
In the aftermath of an adventure the Sixth Corsair shared with Team TARDIS, she controlled her ship by way of an old-fashioned steering wheel. (COMIC: Old Friends)

It was ultimately destroyed and eaten by House after it fell into the bubble universe occupied by the entity, which drained it of its artron energy after removing its matrix. (TV: The Doctor's Wife)

Model and type
The Esperanza was a Type 60 TARDIS. This meant it lacked certain refinements present in other models of TARDISes. (PROSE: One Virtue, and a Thousand Crimes)

Exterior
The Esperanza had a functional chameleon circuit, thusly resembling a pirate ship (PROSE: One Virtue, and a Thousand Crimes) whenever it was practical — and even when it wasn't — because "small, piratical sailing ships [were] Cool". (PROSE: Eleven Things You Probably Didn't Know About the Corsair)