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 Now for My Next Trick...)