Self-conceit; boastfulness (7)
I believe the answer is:
egotism
I believe this clue is a double definition.
'self-conceit' is the first definition.
(I've seen this before)
'boastfulness' is the second definition.
(thesaurus)
(Other definitions for egotism that I've seen before include "Self-centredness" , "Excessive conceit" , "Selfishness" , "Self-importance" , "Items go (anag.)" .)