Bigoted Blair lie damaged Labour's leader (9)
I believe the answer is:
illiberal
'bigoted' is the definition.
(I've seen this in another clue)
'blair lie damaged labour's leader' is the wordplay.
'damaged' is an anagram indicator.
'labour's leader' becomes 'l'.
'blair'+'lie'='blairlie'
'blairlie' with letters rearranged gives 'illibera'.
'illibera'+'l'='ILLIBERAL'
(Other definitions for illiberal that I've seen before include "Reactionary - mean" , "Intolerant; reactionary" , "Narrow-minded" , "Intolerant; ungenerous" , "Restrictive" .)