Gluttonous Greek eyed nervously (6)
I believe the answer is:
greedy
'gluttonous' is the definition.
(similar in meaning)
'greek eyed nervously' is the wordplay.
'greek' becomes 'gr'.
'nervously' is an anagram indicator.
'eyed' is an anagram of 'eedy'.
'gr'+'eedy'='GREEDY'
(Other definitions for greedy that I've seen before include "Gluttonous" , "Overeating" , "Grasping" , "pig!" , "Over-desirous of food" .)