Independent gives one rubbish about right (9)
I believe the answer is:
sovereign
'independent' is the definition.
('sovereign' can be a synonym of 'independent')
'gives one rubbish about right' is the wordplay.
'rubbish' indicates an anagram.
'about' indicates putting letters inside.
'right' becomes 'r' (common abbreviation).
'gives'+'one'='givesone'
'givesone' is an anagram of 'soveeign'.
'soveeign' going around 'r' is 'SOVEREIGN'.
(Other definitions for sovereign that I've seen before include "Supreme ruler" , "Outstanding" , "Old gold coin" , "Monarch - old coin" , "Her Maj?" .)