Eh, it's complicated. Because of the timing with Eccleston, and the budget for the time, Tennant didn't get a new Tardis.
Same thing happened with Capaldi, by the way. Smith blew through two interiors (change in filming location, IIRC), so they didn't budget a new interior for that changeover.
The point being that while I understand the production reasons for these things, I am a little miffed that one of the great joys that we usually get with the new Doctor (the other two being the wardrobe and the characterizations) won't be present when Gatwa takes over. It's a small thing, obviously, but you always want to give every new Doctor a clean slate to work with as much as possible.