Garment beginning to smell, not completely dry (4)
I believe the answer is:
sari
'garment' is the definition.
(sari is a kind of garment)
'beginning to smell not completely dry' is the wordplay.
'beginning to' suggests taking the first letters.
'not completely' means to remove the last letter.
'dry' becomes 'arid' ('arid' can be similar in meaning to 'dry').
The initial letter of 'smell' is 's'.
'arid' with its last letter taken off is 'ari'.
's'+'ari'='SARI'
(Other definitions for sari that I've seen before include "Traditional dress of Indian women" , "Asian dress" , "habit" , "Traditional dress of Hindu women" , "South Asian garment (variant spelling)" .)