When transgression overwhelms key delegate (6)
I believe the answer is:
assign
'delegate' is the definition.
(synonyms)
'when transgression overwhelms key' is the wordplay.
'when' becomes 'as' (eg 'when I walked' means 'as I walked').
'transgression' becomes 'sin' (sin is a kind of transgression).
'overwhelms' indicates putting letters inside.
'key' becomes 'g' (musical key).
'sin' placed around 'g' is 'sign'.
'as'+'sign'='ASSIGN'
(Other definitions for assign that I've seen before include "Allocate, appoint" , "Transfer property" , "Allocate or transfer" , "Transfer or appoint to" , "Allot or ascribe" .)