An odd custom with Eastern dress (7)
I believe the answer is:
costume
'dress' is the definition.
(I know that dress can be written as costume)
'an odd custom with eastern' is the wordplay.
'an odd' indicates anagramming the letters.
'with' is a charade indicator (letters next to each other).
'eastern' becomes 'e'.
'custom' with letters rearranged gives 'costum'.
'costum'+'e'='COSTUME'
(Other definitions for costume that I've seen before include "(Historic etc) dress" , "Attire worn in a play or at a fancy dress ball" , "Actor's set of clothes" , "Rig" , "Outfit" .)