Esperanza

The Esperanza was the Corsair's Type 60 TARDIS, which outwardly resembled a pirate ship thanks to its chameleon circuit. 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)

In the aftermath of the adventure Team TARDIS shared with a female incarnation of the Corsair, the Corsair controlled her ship by way of an old-fashioned steering wheel. (COMIC: Old Friends) It was destroyed and eaten by House after the TARDIS fell into the bubble universe the entity lived in. The entity drained it of its artron energy after removing its matrix. (TV: The Doctor's Wife)

Behind the scenes
The idea of the Corsair's TARDIS being a pirate ship was first mentioned by Neil Gaiman's "Eleven Things You Probably Didn’t Know About The Corsair" in The Brilliant Book 2012.