Start to spin-dry daughter's going away outfit (4)
I believe the answer is:
sari
'away outfit' is the definition.
'sari' can be an answer for 'outfit'. I am not sure about the 'away' bit.
'start to spin-dry daughter's going' is the wordplay.
'start to' suggests taking the first letters.
'dry daughter's going' becomes 'ari' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
The initial letter of 'spin' is 's'.
's'+'ari'='SARI'
(Other definitions for sari that I've seen before include "habit" , "Hindu female garment" , "Traditional dress of Indian women" , "Something worn" , "Indian robe" .)