The Curator

Appearance: The Day of the Doctor
Main actor: Tom Baker

The curator of the National Gallery in London was a mysterious individual who had insight into a particular Time Lord painting.
After the Eleventh Doctor remembered his face (which resembled that of the Fourth Doctor), the curator told him that "in years to come, you might find yourself… revisiting a few. But just the old favourites, eh?"
He spoke with the Eleventh Doctor and told him that the name of the picture was neither No More nor Gallifrey Falls but in fact Gallifrey Falls No More, and pointed the Doctor in the direction of a search for Gallifrey, telling him he had "a lot to do."

The man then suggested that he had perhaps been the Doctor once, or that the Eleventh Doctor had once been him. (TV: The Day of the Doctor)

BEHIND THE SCENES
The script never directly states that this character is an incarnation of the Doctor, but it implies that he may be a future version of the Doctor who has changed back into the form of his fourth incarnation, or is in fact, said previous incarnation. Further fuelling confusion is the fact that Tom Baker is not separately credited for this performance, receiving only a credit for playing "The Doctor" (as did all the other past Doctor actors, who appeared in the episode through the use of archive footage).
Early in the episode Queen Elizabeth I's letter appoints the Doctor as "curator of the Under-Gallery." This and the Doctor giving him a sly wink while they talk are the only hints that the curator may, in fact, be a future incarnation of the Doctor or the Fourth Doctor himself.