Object after hairstyle gets authorisation (6)
I believe the answer is:
permit
'authorisation' is the definition.
(permit is a kind of authorisation)
'object after hairstyle' is the wordplay.
'object' becomes 'it' (pronoun for an inanimate object).
'after' says to put letters next to each other.
'hairstyle' becomes 'perm' (perm is a hairstyle).
'it' after 'perm' is 'PERMIT'.
'gets' acts as a link.
(Other definitions for permit that I've seen before include "Official document giving authorisation" , "Let - pass" , "Warrant" , "Licence -- license" , "Allow; make possible" .)