Ceremonial robe

Ceremonial robes were worn by Time Lords. (PROSE: All Flesh is Grass) When in attendance at the Panopticon, Time Lords wore robes with collar insignia in the colours of their Chapter. Around the time of Goth's assassination of the President, Runcible claimed that the robes were "seldom worn", (TV: The Deadly Assassin) although it seemed in most accounts that most Time Lords ordinarily wore robes when on Gallifrey. (TV: The Invasion of Time, The Day of the Doctor, etc.) Renegade Time Lords who had left the planet, and Gallifreyan agents carrying out missions in the outside universe, could don other outfits when necessary. (TV: Terror of the Autons, Genesis of the Daleks, etc.)

Prior to Gallifrey's destruction, one incarnation of Romana became Lord Cardinal of the Prydonian Chapter and wore their ceremonial robes. (PROSE: Lord Romanadvoratrelundar)

Behind the scenes
The flashback to the Master's initiation seen in The Sound of Drums marked the first appearance of the iconic Time Lord robes in the revived Doctor Who. Tenth Doctor actor David Tennant was photographed wearing the robes over his own costume during filming.