Conceit, self-importance (6)
I believe the answer is:
egoism
This clue is a double definition.
'conceit' is the first definition.
(I've seen this in another clue)
'self-importance' is the second definition.
(thesaurus)
(Other definitions for egoism that I've seen before include "Excessive self-regard" , "self-centred doctrine" , "Self-centredness, vanity" , "principle of self-interest" , "Self-seeking" .)