Possibly airs a dress (4)
I believe the answer is:
sari
'a dress' is the definition.
(I know that sari is a type of dress)
'possibly airs' is the wordplay.
'possibly' indicates anagramming the letters.
'airs' anagrammed gives 'SARI'.
(Other definitions for sari that I've seen before include "Hindu woman's dress" , "Eastern garment" , "Traditional dress of Indian women" , "Hindu female garment" , "Something worn" .)