A magician was a practitioner of magic, either on the stage or ceremonial.
Pulling rabbits out of hats was a trick often performed by stage magicians. (TV: The Sontaran Stratagem, COMIC: The Hat Trick)
Nehra was the magician for a maharaja. He felt threatened by the arrival of the Second Doctor, who he thought was a rival magician. (PROSE: The Steward's Story)
Li H'sen Chang was publicised as a "master of magic and mesmerism". His success was due to the mental powers Magnus Greel bestowed on him. (TV: The Talons of Weng-Chiang)
The 19th century stage magician John Nevil Maskelyne taught the Fourth Doctor sleight of hand. (TV: The Ribos Operation)
Erasmus Darkening was an alien scientist who posed as a magician and alchemist while stranded on Earth in the 17th century. (TV: The Eternity Trap)
Chang used alien science to pose as a magician for his cover while abducting humans for experimentation back on his home world. (PROSE: And for My Next Trick...)
Shortly after his regeneration, the Twelfth Doctor sought to design his new outfit in a minimalist style but noted to the Teller that he had ended up looking like a magician. (TV: Time Heist)
The Mandarin, previously known as the Toymaker, was referred to as "Magician" by the Entity. (PROSE: Games [+]Loading...{"page":"22","1":"Games (short story)"}) The version of the Toymaker who lived in Earth-33⅓, early in his life, received a Paul Daniel's Magic Set which shaped his Doctor Who career. (COMIC: Doctor Who? 196 [+]Loading...["Doctor Who? (DWM 196 comic story)","''Doctor Who?'' 196"])