An overcoat was a form of coat from Earth.
The Doctor's overcoats
Many versions of the Doctor wore overcoats.
After his clothes were ruined by a Xaranti, (PROSE: Deep Blue) the Fifth Doctor wore a silver grey overcoat with peaked lapels and a scarlet trim. (TV: The Awakening-The Caves of Androzani) His successor, the Sixth Doctor, wore the silver overcoat during his first hours; (TV: The Caves of Androzani) before changing for his patchwork frock coat. (TV: The Twin Dilemma)
The Eighth Doctor wore double-breasted overcoats of moleskin with peaked lapels done in bottle green (COMIC: The Pictures of Josephine Day; TV: The Night of the Doctor) or Prussian blue. (AUDIO: He Kills Me, He Kills Me Not) His war successor wore the bottle green one for some time. (TV: The Night of the Doctor; AUDIO: Light the Flame; WC: Doctors Assemble)
The Tenth Doctor wore a double-breasted overcoat of cinnamon brown Alcantara with peaked lapels and a royal blue lining. (TV: The Christmas Invasion-The End of Time)
The Eleventh Doctor wore moleskin overcoats in olive green. (TV: Let's Kill Hitler, The Girl Who Waited, Closing Time, The Wedding of River Song) He also wore a black one when tricking Kahler-Tek. (TV: A Town Called Mercy)
The Twelfth Doctor wore a black overcoat during his showdown with Rassilon. (TV: Hell Bent)
The Thirteenth Doctor wore a black overcoat with peaked lapels. (TV: Spyfall)
The Fourteenth Doctor wore a double-breasted overcoat of navy blue tweed with peaked lapels. (TV: The Power of the Doctor-The Giggle)
The Fifteenth Doctor wore an overcoat of caramel brown tweed with black overchecks and notched lapels when on the lookout for goblins, (TV: The Church on Ruby Road) and when helping residents escape from Finetime. (TV: Dot and Bubble)
The Master's Overcoats
Some versions of the Master wore overcoats.
The Inventor Master wore an asymmetrical black overcoat with a large white lined collar on the left-hand side when he met the First Doctor, Ian Chesterton, Barbara Wright, and Susan Foreman on Destination. (AUDIO: The Destination Wars) He also wore a plain black overcoat during his encounter with the Seventh Doctor and his alliance with the Gods of Ragnarok. (AUDIO: The Psychic Circus)
While posing as the "Other Doctor, the Reborn Master wore an ebony black overcoat. (AUDIO: Dominion)
During his Time War encounter with UNIT and the Cybermen, the War Master wore a maroon moleskin overcoat. (AUDIO: Master of Worlds)
The Spy Master wore a single-breasted overcoat of plum purple cashmere with notched lapels during the Kasaavin invasion, (TV: Spyfall) and the Restoration of the Cyber-Empire. (TV: Ascension of the Cybermen|The Timeless Children) He also wore a black overcoat when posing as Rasputin in St. Petersburg during 1916 as part of his master plan. (TV: The Power of the Doctor)
Companion's Overcoats
Donna Noble wore an army green overcoat during her adventures with the Fourteenth Doctor. (TV: The Star Beast, Wild Blue Yonder, The Giggle)
Jackson Lake wore a single-breasted overcoat of ochre tweed with peaked lapels and a burgundy overcheck when he and Rosita Farisi helped the Tenth Doctor to defeat Cybermen from Pete's World during the 1851 Incident. (TV: The Next Doctor)
Melanie Bush wore an asymmetrical overcoat of beige and ebony tartan when she met the Fourteenth Doctor and Donna Noble, and witnessed the Toymaker’s defeat and the Fifteenth Doctor’s birth. (TV: The Giggle)
Brigadier Alistair Gordon Lethbridge-Stewart wore a double-breasted overcoat in taupe with peaked lapels over his navy blue suit when braving the Game of Rassilon set up by President Borusa in his quest for immortality. (TV: The Five Doctors)
Kate Lethbridge-Stewart, Gordon's daughter, wore a double-breasted overcoat in army green when she met Ruby Sunday in the 2025 of a parallel timeline. (TV: 73 Yards)
Other overcoats
George Ratcliffe, leader of the Association. wore a charcoal overcoat when he and his men dug up the Hand of Omega for the Renegade Daleks. (TV: Remembrance of the Daleks)
Professor Jericho wore a double-breasted overcoat done in ebony black during the year 1904, the 2021 Sontaran Invasion of Earth, and the Flux. (TV: Survivors of the Flux|The Vanquishers)
During the War in Heaven, Ishmael, an Inquisitor of the Order of Tarth'Rioshim, wore a red overcoat which matched his crimson suit. (AUDIO: Call Me Ishmael)
Diagoras wore a charcoal overcoat when he was getting recruits from Hooverville. (TV: Daleks in Manhattan)
The Valeyard wore a copy of the Eighth Doctor's bottle green overcoat. (AUDIO: The War Valeyard)
The Half-Face Man wore an overcoat of plain black wool during the 1890s. (TV: Deep Breath)
The Abzorboloff wore a double breasted overcoat in ebony black with raven black fur on the collar when posing as Victor Kennedy. (TV: Love & Monsters)
Irving Braxiatel wore a black overcoat with his suit. (PROSE: Filthy Lucre, AUDIO: Everybody Loves Irving)
Other references
Gita Chandra recalled being used "like an overcoat" by a "lizard spaceman". (TV: The Vault of Secrets)