Eat a lot too quickly out of hearty greed (5)
I believe the answer is:
feast
'eat' is the definition.
(feasting is a kind of eating)
'quickly out of hearty greed' is the wordplay.
'quickly' becomes 'fast' (synonyms).
'out of' indicates putting letters inside (some letters on the outside of others).
'hearty greed' becomes 'e' (I can't explain this - if you can you should give a lot more credence to this answer).
'fast' going around 'e' is 'FEAST'.
'a lot too' acts as a link.
This may not be correct. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for feast that I've seen before include "Celebratory meal" , "'Enough is as good as a .....'" , "Beano" , "Sumptuous meal" , "Lavish spread" .)