There was an incarnation between the Eighth Doctor & the Ninth Doctor but he didn't use the name Doctor (although he's listed in credits &c as the "War Doctor"). We saw that incarnation briefly in "The Name of the Doctor". In "The Night of the Doctor", we saw the Eighth Doctor regenerate into that incarnation & he featured prominently in "The Day of the Doctor". He was played by John Hurt in all these appearances. A 2014 book entitled "Engines of War" (novel) focuses on this incarnation.