Consented to a selfish desire (6)
I believe the answer is:
agreed
'consented' is the definition.
(agreeing is a kind of consenting)
'a selfish desire' is the wordplay.
'selfish desire' becomes 'greed' (I've seen this before).
'a'+'greed'='AGREED'
'to' is the link.
(Other definitions for agreed that I've seen before include "Accorded" , "Jointly decided" , "That's right" , "Accepted; tallied" , "Did concur" .)