The most common and most likely answer to this crossword clue is the 6 letter word BEEFED
I've seen this crossword clue in The Guardian
B
E
E
F
E
D
Buddy explains!

The straight part
We know that "Grumbled" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case grumbled = beefed.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 BEEFED mean?
BEEFED verb- To complain.
- To add weight or strength to; to beef up.
- To fart; break wind.
- To feud or hold a grudge against.
- To cry
- To fail or mess up.