Excessive self-centredness (8)
I believe the answer is:
egomania
'excessive self-centredness' is the definition.
(I've seen this before)
This is the entire clue.
(Other definitions for egomania that I've seen before include "Morbid self-exaltation" , "Thing about me" , "Obsessive self-concern" , "Obsessive love of oneself" , "form of narcissism" .)