The most common and most likely answer to this crossword clue is the 5 letter word TOQUE
I've seen this crossword clue in Financial Times
T
O
Q
U
E
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 = toque.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 TOQUE mean?
TOQUE noun- A type of hat with no brim.
- (specifically) A tall white hat with no brim of the sort worn by chefs
- (by extension) A chef.
- A variety of bonnet monkey; toque macaque, Macaca sinica.
- An African nominal money of account, equal to 40 cowries.
- A knitted hat, usually conical but of varying shape, often woollen, and sometimes topped by a pom-pom or tassel.
- A rhythm used in Latin music, especially Cuban religious rituals.
- The guitar part of flamenco music.