Greedy eaters keeping one cooking birds (7)
I believe the answer is:
pigeons
'birds' is the definition.
(pigeon is a kind of bird)
'greedy eaters keeping one cooking' is the wordplay.
'greedy eaters' becomes 'pigs' (I am not sure about this - if you are sure you should believe this answer much more).
'keeping' is an insertion indicator.
'cooking' indicates an anagram (cook can mean to falsify or distort).
'one' is an anagram of 'eon'.
'pigs' enclosing 'eon' is 'PIGEONS'.
Can you help me to learn more?
(Other definitions for pigeons that I've seen before include "Town birds" , "Spin ego around the birds" , "Columbiform birds" , "traditional pie filling" , "Cooing birds" .)