Western headgear? I beg your pardon? (4)
I believe the answer is:
what
'i beg your pardon?' is the definition.
(I've seen this before)
'western headgear?' is the wordplay.
'western' becomes 'w'.
'headgear?' becomes 'hat' (hat is a kind of headgear).
'w'+'hat'='WHAT'
(Other definitions for what that I've seen before include "Interrogatory word" , "Eh?" , "I didn't hear" , "I beg your pardon" , "Word used in a question" .)