The most common and most likely answer to this crossword clue is the 5 letter word TERAI
I've seen this crossword clue in The Times
T
E
R
A
I
More clues leading to the result TERAI
Buddy explains!

The straight part
We know that "headgear" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case headgear = terai.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 TERAI mean?
TERAI noun- A belt of marshy land, which lies between the foothills of the Himalayas and the plains.
- A terai hat.