A doubter disposed to be stubborn (8)
I believe the answer is:
obdurate
'stubborn' is the definition.
(obdurate means stubborn or obstinate)
'a doubter disposed' is the wordplay.
'disposed' indicates anagramming the letters.
'a'+'doubter'='adoubter'
'adoubter' with letters rearranged gives 'OBDURATE'.
'to be' acts as a link.
(Other definitions for obdurate that I've seen before include "Stiff-necked" , "Dogged" , "Inflexible" , "Stubbornly persistent" , "Unyielding - cruel" .)