The most common and most likely answer to this crossword clue is the 4 letter word KEPI
I've seen this crossword clue in The Times
K
E
P
I
More clues leading to the result KEPI
- What's worn in Paris maybe by Private Pike back to front
- Hat requiring some dagger-like pins
- Covered by yarmulke, pillbox hat
- Swapped sides of stupid boy’s hat
- Take Pierre’s cover for his service cap
- Some take pity on legionnaire head
- Heads of King Edward’s people in military headgear
- Rogue content in spiked headwear
- Military item of clothing? Some fake piece
- Hat like picador displays
Buddy explains!

The straight part
We know that "Hat" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case hat = kepi.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 KEPI mean?
KEPI noun- A cap with a flat circular top and a visor, particularly associated with French uniforms.