The most common and most likely answer to this crossword clue is the 7 letter word PIGGIES
I've seen this crossword clue in The Daily Telegraph
P
I
G
G
I
E
S
More clues leading to the result PIGGIES
Buddy explains!

The straight part
We know that "Gluttons" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case gluttons = piggies.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 PIGGIES mean?
PIGGIES noun- (hypocoristic) A pig (the animal).
- (hypocoristic) A guinea pig.
- (hypocoristic) A toe.
- (mildly) A pig, a greedy person.
- A member of the police.