The most common and most likely answer to this crossword clue is the 4 letter word CRAM
I've seen this crossword clue in The Daily Telegraph
C
R
A
M
More clues leading to the result CRAM
- Take the middle bit from the best stuff
- Stuff to study
- Stuff remains at the vineyard to be knocked back
- Stuff for starters cooked with butter
- Stuff credit — a source of misery!
- Stuff about sheep
- Eat greedily from hamper, but not quietly
- Revolutionary hurt by constant press
- Stuff made with cold butter?
- Intensively study some basic education in academic stream
Buddy explains!

The straight part
We know that "Eat greedily" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case eat greedily = cram.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does CRAM mean?
CRAM noun- The act of cramming (forcing or stuffing something).
- Information hastily memorized.
- A warp having more than two threads passing through each dent or split of the reed.
- (British slang) A lie; a falsehood.
- A mathematical board game in which players take turns placing dominoes horizontally or vertically until no more can be placed, the loser being the player who cannot continue.
- A small friendship book with limited space for people to enter their information.
- To press, force, or drive, particularly in filling, or in thrusting one thing into another; to stuff; to fill to superfluity.
- To fill with food to satiety; to stuff.
- To put hastily through an extensive course of memorizing or study, as in preparation for an examination.
- To study hard; to swot.
- To eat greedily, and to satiety; to stuff oneself.
- (British slang) To lie; to intentionally not tell the truth.
- (British slang) To make (a person) believe false or exaggerated tales.