Monster to look greedily left to right (4)
I believe the answer is:
ogre
'monster' is the definition.
(synonyms)
I don't understand how the rest of the clue works.
Can you help me to learn more?
(Other definitions for ogre that I've seen before include "stern one who inspires fear" , "man-eater" , "ugly one" , "Monstrous creature" , "Evil giant" .)