A t-shirt was an item of clothing.
Rose Tyler wore t-shirts done on grey, (TV: Rose) pink, (TV: Aliens of London/World War Three) Union flag, (TV: The Empty Child/The Doctor Dances) a blue Wichita Falls t-shirt, (TV: The Girl in the Fireplace) mustard, (TV: Fear Her) black (TV: Army of Ghosts/Doomsday) and rose. (TV: Partners in Crime, Turn Left, The Stolen Earth/Journey's End)
Under her lilac blue trench coat, the Thirteenth Doctor wore a variety of similarly designed t-shirts with rainbow stripes running across their chest, such as a low collar navy blue shirt, (TV: The Woman Who Fell to Earth) a dark pink low collar shirt, (TV: Rosa) a dark pink crew collar shirt, (TV: The Tsuranga Conundrum) a navy blue crew collar t-shirt with a smeared rainbow pattern, (TV: Kerblam!) light blue crew collar shirt, (TV: Resolution) and a dark purple crew collar shirt. (TV: Revolution of the Daleks)
After avoiding his own death at Lake Silencio, River Song bought the Eleventh Doctor a t-shirt saying "I died at Lake Silencio and all my wife got me was this lousy t-shirt". (PROSE: Houdini and The Space Cuckoos)