Trenchcoat

The Fifteenth Doctor's burnt orange double breasted trenchcoat. (PROSE: "Heroes of Time" ^[+]Part of Whotopia: The Ultimate Guide to the Whoniverse, Loading...{"namedpart":"Heroes of Time","1":"Whotopia: The Ultimate Guide to the Whoniverse (reference book)"})

Trenchcoats' were coats made for protection from weather, famously worn on wars.

Worn by the Doctor

The Fourth Doctor wore a single-breasted trenchcoat of plum purple velvet when he and Romana II foil Tryst's conversion of Mandrels into Vraxoin. (TV: Nightmare of Eden) He also wore a burgundy trenchcoat, (TV: The Leisure Hive) up to his death. (TV: Logopolis) His successor, the Fifth Doctor, wore it before switching for a beige frock coat with scarlet trim. (TV: Logopolis, Castrovalva)

The Seventh Doctor wore a black leather trenchcoat on Nazi Germany. (PROSE: Timewyrm: Exodus)

The War Doctor wore double-breasted leather trenchcoats on black (COMIC: The Whole Thing's Bananas) or brown. (COMIC: The Clockwise War, The Lost Dimension, Four Doctors; TV: The Name of the Doctor, The Day of the Doctor)

In World War I, the Ninth Doctor wore a British Army trenchcoat. (COMIC: The Forgotten)

The Thirteenth Doctor wore a hooded, periwinkle trenchcoat with midnight blue interim, apart from the sleeves, which had lavender insides, and a rainbow pattern along the edges. (TV: The Woman Who Fell to Earth-The Power of the Doctor)

The Fifteenth Doctor frequently wore a double-breasted trenchcoat of burnt orange leather. (PROSE: "Heroes of Time" ^[+]Part of Whotopia: The Ultimate Guide to the Whoniverse, Loading...{"namedpart":"Heroes of Time","1":"Whotopia: The Ultimate Guide to the Whoniverse (reference book)"})

Worn by companions

Sarah Jane Smith occasionally wore trenchcoats. (TV: Eye of the Gorgon, The Last Sontaran, The Mark of the Berserker, et al.)

Amy Pond wore a dark teal trenchcoat during her encounter with Vincent van Gogh. (TV: Vincent and the Doctor)

Donna Noble wore a single-breasted trenchcoat of tan leather. (TV: Turn Left, The Stolen Earth/Journey's End)

Martha Jones wore a double-breasted trenchcoat of charcoal grey leather with her mauve tank top. (TV: Reset)

Susan Foreman wore a beige trenchcoat during the Game of Rassilon. (TV: The Five Doctors)

Worn by the Master

The Master wore trenchcoats in some incarnations.

The Bruce Master wore a black leather trenchcoat during the 2223 Dalek invasion of Earth. (AUDIO: Faustian-Passion)

The Spy Master wore a double-breasted trenchcoat of black leather when posing as a Nazi in Paris. (TV: Spyfall) He also wore the Thirteenth Doctor's trenchcoat when processing her body as part of his master plan. (TV: The Power of the Doctor)

Worn by others

Detective Duggan wore a beige trenchcoat when he helped the Fourth Doctor and Romana II. (TV: City of Death)

Sally Sparrow wore a dark brown trenchcoat during her first encounter with Weeping Angels. (TV: Blink)

Vienna Salvatori who dwelled during the 2223 Dalek invasion of Earth wore leather trenchcoats done in navy, (AUDIO: The Shadow Heart-Vengeance) or ebony black. (AUDIO: The Nemesis Express-Passion)

Kate Stewart wore a beige trenchcoat during (TV: The Power of Three) the Year of the Slow Invasion. (PROSE: The Whoniverse) She also wore a raven black trenchcoat during the 1562/2013 Zygon invasion of Earth. (TV: The Day of the Doctor)

The Second Rani wore a black trenchcoat when posing as Professor Baxton. (AUDIO: The Rani Elite, Planet of the Rani)

One version of the Corsair with a bowler hat wore a black trenchcoat. (PROSE: Eleven Things You Probably Didn't Know About the Corsair)