A gilet was a light sleeveless padded jacket for warmth.
River Song wore a sheepskin gilet during the Total Collapse Event Incident. (TV: The Pandorica Opens/The Big Bang)
Shona McCullough, Ashley Carter, Rona Bellows, and Albert Smithe wore gilets when dreaming they were scientists on the North Pole during Christmas Eve because of dream crabs. (TV: Last Christmas)