They claim to be clairvoyant (8)
I believe the answer is:
psychics
(Other definitions for psychics that I've seen before include "People with occult powers like mediums" , "They claim to have occult powers of communication with the dead" , "They claim to have extrasensory perception or occult powers" , "Spiritualists or mediums" , "People who claim to be able to contact the dead" .)