Admitted a craving (6)
I believe the answer is:
agreed
'admitted' is the definition.
(I've seen this before)
'a craving' is the wordplay.
'craving' becomes 'greed' (greed is craving too much).
'a'+'greed'='AGREED'
(Other definitions for agreed that I've seen before include "In accord" , "Let's do it!" , "Shared an opinion" , "That's right" , "Acceded" .)