Possibly airs dress (4)
I believe the answer is:
sari
'dress' is the definition.
(sari is a kind of dress)
'possibly airs' is the wordplay.
'possibly' is an anagram indicator.
'airs' anagrammed gives 'SARI'.
(Other definitions for sari that I've seen before include "Indian costume" , "Traditional dress of Hindu women" , "Indian robe" , "habit" , "Hindu female garment" .)