Self-importance is so not right (3)
I believe the answer is:
ego
'self-importance' is the definition.
('ego' can be a synonym of 'self-importance')
'so not right' is the wordplay.
'so' becomes 'ergo' ('ergo' can be a synonym of 'so').
'not' indicates named letters should be taken away.
'right' becomes 'r' (common abbreviation).
'ergo' with 'r' removed is 'EGO'.
'is' is the link.
(Other definitions for ego that I've seen before include "One's sense of self-importance" , "number one" , "One's image of oneself" , "Conceit - the Latin "I"" , "Inflated pride" .)