Conceited people (8)
I believe the answer is:
egotists
'conceited people' is the definition.
(I've seen this in another clue)
This is the entire clue.
(Other definitions for egotists that I've seen before include "They have an exaggerated sense of their own importance" , "Self-centred self-seekers" , "The selfish" , "People with exaggerated notions of their own importance" , "Conceited and self-centered people" .)