Exceptional arbiter’s primarily real legal expert (9)
I believe the answer is:
barrister
'legal expert' is the definition.
(thesaurus)
'exceptional arbiter's primarily real' is the wordplay.
'exceptional' is an anagram indicator (an unusual or exceptional ordering of the letters).
'primarily' suggests taking the first letters.
The first letter of 'real' is 'r'.
'arbiters' is an anagram of 'barriste'.
'barriste'+'r'='BARRISTER'
(Other definitions for barrister that I've seen before include "Legal representative" , "Rarest rib for the eminent lawyer" , "American lawyer" , "Legal counsel" , "A bewigged legal eagle" .)