The most common and most likely answer to this crossword clue is the 3 letter word FEZ
F
E
Z
More clues leading to the result FEZ
Buddy explains!

The straight part
We know that "Cooper’s hat" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case cooper’s hat = fez.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 FEZ mean?
FEZ noun- A felt hat in the shape of a truncated cone, having a flat top with a tassel attached.