Green food almost entirely rejected: beginning on eggs (5)
I believe the answer is:
naive
'green' is the definition.
(green can mean naive or innocent)
'food almost entirely rejected beginning on eggs' is the wordplay.
'food' becomes 'viand' (archaic term for food).
'almost entirely' means to remove the last letter.
'rejected' says the letters should be written backwards.
'beginning on eggs' becomes 'e' (I can't explain this - if you can you should believe this answer much more).
'viand' with its final letter removed is 'vian'.
'vian' in reverse letter order is 'naiv'.
'naiv'+'e'='NAIVE'
(Other definitions for naive that I've seen before include "Simple-minded" , "Lacking guile" , "Lacking judgment" , "Credulous, unworldly" , "Simple in outlook" .)