The writer's shame, concealing base wickedness (7)
I believe the answer is:
impiety
'wickedness' is the definition.
(thesaurus)
'the writer's shame concealing base' is the wordplay.
'the writer's' becomes 'Im' ('I am' referring to the writer of the clue).
'shame' becomes 'pity' (synonyms).
'concealing' is an insertion indicator.
'base' becomes 'e' (mathematical symbol).
'pity' placed around 'e' is 'piety'.
'im'+'piety'='IMPIETY'
(Other definitions for impiety that I've seen before include "sacrilege" , "Lack of reverence" , "Irreverence, profanity" , "godlessness" , "Irreligion" .)