The most common and most likely answer to this crossword clue is the 6 plus 2 plus 3 plus 6 letter word SNOUTS IN THE TROUGH
I've seen this crossword clue in The Guardian
S
N
O
U
T
S
I
N
T
H
E
T
R
O
U
G
H
Buddy explains!
The straight part
We know that "What greedy types have" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case what greedy types have = snouts in the trough.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.