Sorry self-importance is elevated in rigged Capitol (10)
I believe the answer is:
apologetic
'sorry' is the definition.
(saying sorry)
'self-importance is elevated in rigged capitol' is the wordplay.
'self-importance' becomes 'ego' (synonyms).
'is elevated' is a reversal indicator (in a down clue, letters go up).
'in' indicates putting letters inside.
'rigged' indicates anagramming the letters.
'ego' backwards is 'oge'.
'capitol' is an anagram of 'apoltic'.
'oge' put into 'apoltic' is 'APOLOGETIC'.
(Other definitions for apologetic that I've seen before include "Expressing regret" , "in sorry state" , "Regretful" , "Regretfully admitting fault" , "Acknowledging faults" .)