From Tardis Wiki, the free Doctor Who reference

Gloves were garments worn on hands, for style or protection.

The First Doctor wore fingerless gloves on cold times; (TV: An Unearthly Child, etc) right up to his death after the 1986 Cyberman Invasion of Earth. (TV: The Tenth Planet, Twice Upon A Time)

The Third Doctor sometimes wore riding gloves while driving Bessie (TV: Doctor Who and the Silurians) or outdoors in general. (TV: The Claws of Axos)

The Fourth Doctor wore silver grey gloves when he met Magnus Greel in London during 1892. (TV: The Talons of Weng-Chiang)

Yasmin Khan wore tan leather gloves during the year 1904, the 2021 Sontaran Invasion of Earth, and the Flux. (TV: Survivors of the Flux, The Vanquishers)

The Master wore black leather gloves in his UNIT form (TV: Terror of the Autons-Frontier in Space) and Bruce incarnations, (AUDIO: The Shadow Heart-Passion) as well as tan ones in his war one. (AUDIO: Killing Time) He also wore black velvet gloves in his Tremas form. (TV: The Keeper of Traken-Survival) The Saxon incarnation of the Master also wore black gloves as part of his outdoor dress. (TV: The Sound of Drums, Last of the Time Lords)

Rose Tyler wore cherry, fingerless gloves during her second visit to Cardiff and the Cardiff Earthquake, (TV: Boom Town) and purple fingerless gloves on the windswept beach at Bad Wolf Bay in what she believed would be her final farewell to the Tenth Doctor after being trapped in a parallel world. (TV: Doomsday)

Vienna Salvatori wore black gloves without fingers. (AUDIO: The Shadow Heart-Vengeance)

Jenny Flint wore chocolate brown leather gloves during the Battle of Demons Run. (TV: A Good Man Goes to War)

Malohkeh, the chief scientist of Eldane's Silurian colony, wore protective gloves; (TV: The Hungry Earth / Cold Blood) as did a parallel version who served as a physician for Holy Roman Emperor Winston Churchill on River Song's World. (TV: The Wedding of River Song)

Lieutenant Harry Sullivan, a doctor from UNIT, wore ebony leather gloves when posing as a member of the Ministry of Defence to question the National Institute for Advanced Scientific Research. (TV: Robot)

The Ringmaster of the Psychic Circus wore white gloves. (TV: The Greatest Show in the Galaxy)

The Pied Piper wore white gloves when posing as Mr. Spellman, director of Spellman's Magical Museum of the Circus. (TV: The Day of the Clown)

The resurrection gauntlet was described as a glove. (TV: Everything Changes, They Keep Killing Suzie, Dead Man Walking)

The Fifteenth Doctor created a pair of intelligent gloves that could invert the weight of any object. (TV: The Church on Ruby Road [+]Loading...["The Church on Ruby Road (TV story)"])