Heartlessly craving something extra (8)
I believe the answer is:
addition
'something extra' is the definition.
(I've seen this before)
'heartlessly craving' is the wordplay.
'heartlessly' suggests removing the centre.
'craving' becomes 'addiction' (addiction is a kind of craving).
'addiction' with its centre removed is 'ADDITION'.
(Other definitions for addition that I've seen before include "plus" , "One of the four basic planks of arithmetic" , "Increment" , "Mathematical process" , "Something extra" .)