The most common and most likely answer to this crossword clue is the 8 letter word EDACIOUS
I've seen this crossword clue in The Times
E
D
A
C
I
O
U
S
Buddy explains!

The straight part
We know that "Greedy" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case greedy = edacious.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 EDACIOUS mean?
EDACIOUS adjective- Having an insatiable appetite; voracious, ravenous, piggish.