A psychiatrist was a physician that diagnosed and treated mental disorders in sentient lifeforms.
Sabalom Glitz tried to kill his prison psychiatrist, after which the psychiatrist diagnosed Glitz as having a "deep-rooted maladjustment". (TV: The Mysterious Planet)
Freya Gabriel was a psychiatrist who used hypnotic regression therapy on CP Doveday, to find out his true origin. She placed the Seventh Doctor in a straight jacket, so she could question him. (AUDIO: Lurkers at Sunlight's Edge)
In the early 20th century London, Major Aske claimed to be Repple's psychiatrist. (PROSE: The Clockwise Man)
In the Royal Hope Hospital, after the Tenth Doctor (disguised as a patient) related his adventures with Benjamin Franklin, Mr Stoker recommended a visit from the psychiatrist. (TV: Smith and Jones)
The Zygon Kritakh forgot his true identity and began to believe he was the human he was impersonating, Michael Kirkwood. In the early 21st century, he went to see a psychiatrist to help him with his dreams of being a Zygon. (HOMEVID: Zygon: When Being You Just Isn't Enough)
Parallel universe
Christine was a psychiatrist who attempted to treat a young Amelia Pond's belief in celestial objects other than the sun. In that alternative timeline, the explosion of the TARDIS had destroyed all the stars in the universe. (TV: The Big Bang)