An idea of self-importance (7)
I believe the answer is:
conceit
This clue is a double definition.
'an idea' is the first definition.
(thesaurus)
'self-importance' is the second definition.
(thesaurus)
'of' is the link.
(Other definitions for conceit that I've seen before include "Fanciful notion; self-pride" , "Vanity; fanciful notion" , "Fanciful notion; excessive pride in oneself" , "Overbearing self-esteem" , "Excessive self-pride" .)