A man let rip about law-making authority (10)
I believe the answer is:
parliament
'law-making authority' is the definition.
(parliament makes laws)
'a man let rip about' is the wordplay.
'about' is an anagram indicator.
'a'+'man'+'let'+'rip'='amanletrip'
'amanletrip' anagrammed gives 'PARLIAMENT'.
(Other definitions for parliament that I've seen before include "Houses" , "Legislative assembly" , "The law is laid down here" , "Legislative body" , "UK legislature" .)