Waistcoat

A waistcoat was an article of clothing.

Worn by the Doctor
Many incarnations of the Doctor wore waistcoats.

The First Doctor wore a beige tweed waistcoat with a fob watch. (TV: An Unearthly Child, The Daleks, etc.)

The Third Doctor wore a grey waistcoat with symbols. (TV: The Curse of Peladon)

The Fourth Doctor wore waistcoats with cheques and fob watches. (TV: Terror of the Zygons, onwards)

The Sixth Doctor wore waistcoats on many styles with a green fob watch. (TV: The Twin Dilemma)

Right up to his death, the Seventh Doctor wore a scarlet brocade waistcoat. (TV: Doctor Who)

The Eighth Doctor wore some double breasted waistcoats of paisley-brocade. (TV: Doctor Who) Soon, he wore single breasted waistcoats of mustard velvet (COMIC: The Pictures of Josephine Day) or bronze paisley-brocade. (TV: The Night of the Doctor)

The War Doctor wore double-breasted moleskin waistcoats with fob watches under his leather trench coats. (TV: The Day of the Doctor, etc)

During his retirement to the Victorian era, the Eleventh Doctor wore a battered felt top hat, a burgundy frock coat, a velvet waistcoat with collars and a pocket watch with a fob chain. (TV: The Great Detective, The Snowmen) He wore the same outfit before his death. (TV: The Time of the Doctor)

The Twelfth Doctor sometimes wore waistcoats. (TV: Mummy on the Orient Express, Thin Ice)

The Thirteenth Doctor wore a blue waistcoat with clock symbols during her first encounter with Ashad. (TV: The Haunting of Villa Diodati)

Worn by companions
Sarah Jane Smith sometimes wore waistcoats. (TV: The Last Sontaran, onwards)

Romana II wore a gold waistcoat. (TV: The Horns of Nimon)

Ryan Sinclair and Graham O'Brien sometimes wore waistcoats. (TV: Nikola Tesla's Night of Terror, The Haunting of Villa Diodati)

Yasmin Khan wore a beige waistcoat with her ivory shirt and her bottle green walking suit. (TV: Survivors of the Flux, The Vanquishers)

While acting as his successor, Jack Harkness wore the Sixth Doctor's coat, including his seventh favourite waistcoat and yellow-stripped trousers. (AUDIO: Piece of Mind)

Worn by Others
The Master wore waistcoats during his Tremas (TV: Survival), war (AUDIO: Only the Good) and spy incarnation. (TV: Spyfall)

Jenny Flint wore single breasted waistcoats done in blue (TV: A Good Man Goes to War) or grey. (COMIC: The Lost Dimension)

Emily Morris wore a cream waistcoat with tan stripes. (TV: Lost in Time)

Henry Jago and George Litefoot wore double breasted waistcoats. (TV: The Talons of Weng-Chiang)

When he thought he was the Doctor, Jackson Lake wore a double breasted waistcoat of scarlet brocade under his tweed overcoat. (TV: The Next Doctor)