Permit woman, as ordered (4)
I believe the answer is:
visa
'permit' is the definition.
(I know that visa is a more specific form of authorise)
'woman as ordered' is the wordplay.
'woman' becomes 'Vi' (short for Violet).
'ordered' is an anagram indicator.
'as' anagrammed gives 'sa'.
'vi'+'sa'='VISA'
(Other definitions for visa that I've seen before include "It allows the bearer to enter the country issuing it" , "ID" , "Passport stamp or well-known credit card" , "Travel permit stamped in passport etc" , "Travel stamp in passport" .)