Judge's ultimate trait is fairness (8)
I believe the answer is:
equality
'is fairness' is the definition.
(thesaurus)
'judge's ultimate trait' is the wordplay.
'ultimate' indicates one should take the final letters.
'trait' becomes 'quality'.
The last letter of 'judge' is 'e'.
'e'+'quality'='EQUALITY'
(Other definitions for equality that I've seen before include "No favouritism being shown" , "level playing field" , "correspondence" , "policy of left-wingers" , "It shows no favours" .)