The most common and most likely answer to this crossword clue is the 4 letter word CAPO
I've seen this crossword clue in The Times
C
A
P
O
More clues leading to the result CAPO
- Top police officers advancing caught mobster
- Don headgear: sombrero’s back
- Godfather chopping tail off fowl
- Leader of criminals on an Italian river?
- Mafia leader's way of raising the tone?
- Hat on old Mafia boss
- Top on head of Mafia
- Mostly chicken gangland boss
- Criminal boss is firm about the old man retiring
- Mobster corrupting American cop
Buddy explains!

The straight part
We know that "Mafia leader/way of raising the tone" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case mafia leader/way of raising the tone = capo.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 CAPO mean?
CAPO noun- A movable bar placed across the fingerboard of a guitar used to raise the pitch of all strings.
- A leader in the Mafia; a caporegime.
- A leader and organizer of supporters at a sporting event, particularly association football matches.