Beard

A beard was a form of hair growth on one's face. They were often shortened to just thick upper lip hair known as a moustache.

The Master often wore one (TV: Terror of the Autons et al.) known as a goatee. (COMIC: The Judas Goatee) It led to the Fifth Doctor asking the Tenth if he "still had that rubbish beard". The Tenth Doctor replied that he had a wife instead. (TV: Time Crash)

The Doctor is here making reference to the slang term meaning a woman who accompanies a gay man to give the impression that he's straight.

Charles Dickens had one when he met the Ninto Doctor and Rose. (TV: The Unquiet Dead)

The Doctor in his incarnation known as the War Doctor grew a beard, (TV: The Name of the Doctor, The Day of the Doctor) something that'd happen again in his later years as Muldwych. (PROSE: Birthright, Happy Endings) The Eleventh Doctor would grow a beard when held in captivity for significant periods of time. (TV: Day of the Moon, The Wedding of River Song)

Varun Singh had one grown due to the practice of Kesh in Sikhism. (TV: For Tonight We Might Die, The Coach with the Dragon Tattoo, Brave-ish Heart)