A psychiatrist was a physician that diagnosed and treated mental disorders in sentient lifeforms.
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)
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 Edit
Christine was a psychiatrist who attempted to treat a young Amelia Pond's belief in celestial objects other than the sun. In that alternate timeline, the explosion of the TARDIS had destroyed all the stars in the universe. (TV: The Big Bang)