The most common and most likely answer to this crossword clue is the 5 letter word MITRE
I've seen this crossword clue in Financial Times
M
I
T
R
E
More clues leading to the result MITRE
- Child carrying king’s headgear
- Some permit required for coverage of a primate?
- One identifies bishop and rook pocketed by small child
- Send cycling headgear for the bishop!
- Could a reporter cover for a bishop?
- Joint area of responsibility when cycling around
- Starts to moan, injuring the right elbow joint
- King dressed in kid’s hat
- Joint that goes to a bishop’s head!
- Pope’s belt and pointed headdress
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 = mitre.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 MITRE mean?
MITRE noun- A covering for the head, worn on solemn occasions by church dignitaries, which has been made in many forms, mostly recently a tall cap with two points or peaks.
- The surface forming the bevelled end or edge of a piece where a miter joint is made; also, a joint formed or a junction effected by two beveled ends or edges; a miter joint.
- A 13th-century coin minted in Europe which circulated in Ireland as a debased counterfeit sterling penny, outlawed under Edward I.
- A cap or cowl for a chimney or ventilation pipe.
- A gusset in sewing, etc.
- A square with one triangular quarter missing from the outside.
- To adorn with a mitre.
- To unite at an angle of 45°.