Consented to give up a vice (5)
I believe the answer is:
greed
'vice' is the definition.
(I've seen this before)
'consented to give up a' is the wordplay.
'consented to' becomes 'agreed' (agreeing is a kind of consenting to).
'give up' is a deletion indicator.
'agreed' with 'a' taken out is 'GREED'.
(Other definitions for greed that I've seen before include "Vice" , "Selfish desire" , "Insatiability" , "Avidity" , "Rapacity" .)