Consented to a deadly sin (6)
I believe the answer is:
agreed
'consented' is the definition.
(agreeing is a kind of consenting)
'a deadly sin' is the wordplay.
'deadly sin' becomes 'greed' (greed is a kind of deadly sin).
'a'+'greed'='AGREED'
'to' is the link.
(Other definitions for agreed that I've seen before include "very well" , "Settled by common consent" , "Jointly decided" , "Harmonised" , "Assented, acquiesced" .)