Type 53

Type 53 was a type of TARDIS used by Time Lords and more advanced than the Type 40s. The First Doctor nearly borrowed/stole a Type 53 while leaving Gallifrey with his granddaughter, but was convinced by an echo of Clara Oswald to pick the Type 40 because the "navigation system [was] knackered" and "[he would] have much more fun" with it. During the conversation, Susan had already entered the capsule before the Doctor called her back out. (TV: The Name of the Doctor, COMIC: Hungry Thirsty Roots)

According to another account, the First Doctor nearly stole the Type 53 while alone, but dismissed it as "new-fangled [and] soulless" and went in favour of the Type 40. The Doctor found the Type 53 TARDIS on a construction palette with its specifications listed while the Type 40 was not far away. (PROSE: Lungbarrow)

Despite being newer than the Doctor's TARDIS, the Eleventh Doctor described it as "crummy [and] old". (COMIC: Hungry Thirsty Roots)