Stopping insatiable appetite, nothing beyond a kilo for classic beauty (5,3)
I believe the answer is:
greek god
'classic beauty' is the definition.
(god from classical times)
'stopping insatiable appetite nothing beyond a kilo' is the wordplay.
'stopping' indicates putting letters inside (stopping can mean blocking a gap).
'insatiable appetite' becomes 'greed' (greed is excessive appetite).
'nothing' becomes 'O' (looks like zero - 0).
'beyond' means one lot of letters go next to another.
'a kilo' becomes 'kg' ('kg' can be a synonym of 'kilo').
'o' after 'kg' is 'kgo'.
'greed' enclosing 'kgo' is 'GREEK GOD'.
'for' acts as a link.
(Other definitions for greek god that I've seen before include "Pan, for example" , "dish" .)