The most common and most likely answer to this crossword clue is the 4 letter word DOGE
I've seen this crossword clue in The Guardian
D
O
G
E
More clues leading to the result DOGE
- Italian official returned for one binge with ill effects
- Setter maybe heading for encomium? That's official
- Magistrate’s heartless act that is dishonest
- Heartlessly trick old Venetian
- Magistrate in Venice finally meeting man’s best friend
- Big cheese from Italy to follow starter of eggs
- Avoid neglecting duke and foreign magistrate
- Magistrate’s trick, being heartless
- Cheat, say, repelled magistrate
- The Gods are a bit cut up with the lawgiver
Buddy explains!

The straight part
We know that "Big cheese from Ital/y" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case big cheese from ital/y = doge.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 DOGE mean?
DOGE noun- The chief magistrate in the republics of Venice and Genoa.
- A dog.
- Specifically, a Shiba Inu, as in the doge meme.