The most common and most likely answer to this crossword clue is the 11 plus 3 letter word DEERSTALKER HAT
I've seen this crossword clue in The Guardian
D
E
E
R
S
T
A
L
K
E
R
H
A
T
More clues leading to the result DEERSTALKER HAT
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 = deerstalker hat.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.