The most common and most likely answer to this crossword clue is the 4 letter word DORK
I've seen this crossword clue in Financial Times
D
O
R
K
More clues leading to the result DORK
Buddy explains!

The straight part
We know that "idiot" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case idiot = dork.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 DORK mean?
DORK noun- A long Scottish dagger with a straight blade.
- (Midwest US) A penis; dork.
- (Midwest US) A socially unacceptable person; an oddball.