Possibly airs a dress (4)
I believe the answer is:
sari
'a dress' is the definition.
(sari is a kind of dress)
'possibly airs' is the wordplay.
'possibly' is an anagram indicator.
'airs' with letters rearranged 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" .)