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 an adventure an incarnation of the Corsair shared whith 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)

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. According to it, the Corsair's TARDIS looked like a pirate ship whenever it was practical and sometimes when it was impractical.