Fixed ado with brute that's stubborn (8)
I believe the answer is:
obdurate
'stubborn' is the definition.
(obdurate means stubborn or obstinate)
'fixed ado with brute' is the wordplay.
'fixed' indicates an anagram.
'with' means one lot of letters go next to another.
'ado' after 'brute' is 'bruteado'.
'bruteado' anagrammed gives 'OBDURATE'.
'that's' is the link.
(Other definitions for obdurate that I've seen before include "Unyielding - cruel" , "hard to influence" , "Dogged" , "Inflexible" , "Stubborn, unpersuadable" .)