Unauthorised act ordered by savage (7)
I believe the answer is:
wildcat
'unauthorised' is the definition.
('wildcat' can be a synonym of 'unauthorized')
'act ordered by savage' is the wordplay.
'ordered' indicates an anagram.
'by' says to put letters next to each other.
'savage' becomes 'wild' ('wild' can be similar in meaning to 'savage').
'act' with letters rearranged gives 'cat'.
'cat' after 'wild' is 'WILDCAT'.
(Other definitions for wildcat that I've seen before include "Ferocious person" , "financially unsound?" , "Unauthorised - animal" , "Lynx, for example" , "Well, kind of" .)