James T. Kirk

In a parallel universe, James T. Kirk was the captain the USS Enterprise in the 23rd century.

On one occasion, the Eleventh Doctor recalled memories of his fourth incarnation meeting up with Kirk and the command crew of the USS Enterprise to combat a Cyberman invasion of Aprilia III. (IDW: Assimilation²)

Other references
Captain Kirk was also the name of a fictional character who existed in the Doctor's universe. When DI Patricia Menzies entered the Sixth Doctor's TARDIS and saw its console room in 2010, she commented that she had expected the TARDIS interior to resemble "Captain Kirk's ship." The Doctor responded: "Detective Inspector, may I tell you something and I can't stress this enough: I am not Captain Kirk." (BFA: The Crimes of Thomas Brewster)

Behind the scenes
The mention of Captain Kirk in The Crimes of Thomas Brewster treats him as a fictional character (as do, implicitly, other references to Star Trek and Star Trek: The Next Generation in Doctor Who stories). Assimilation², of course, treats him as a "real" individual. Reconciling these diegetic levels is an exercise best left to the reader.