For example, Oscar’s sense of self-importance (3)
I believe the answer is:
ego
'sense of self-importance' is the definition.
(one's sense of self)
'for example oscar's' is the wordplay.
'for example' becomes 'eg' (short for 'exempli gratia', 'for example' in Latin).
'oscar' becomes 'O' (phonetic alphabet: alpha, bravo, charlie etc.).
'eg'+'o'='EGO'
(Other definitions for ego that I've seen before include "(Person's) sense of self-esteem" , "One's image of oneself" , "One's self image" , "Person's sense of self" , "Sense of self, conceit" .)