Convert a doubter? That's hard (8)
I believe the answer is:
obdurate
'hard' is the definition.
(thesaurus)
'convert a doubter?' is the wordplay.
'convert' indicates an anagram (I've seen this in other clues).
'a'+'doubter'='adoubter'
'adoubter' with letters rearranged gives 'OBDURATE'.
'that's' is the link.
(Other definitions for obdurate that I've seen before include "Unyielding - cruel" , "Stubbornly resistant" , "Stiff-necked" , "Stubborn, unpersuadable" , "Obstinate and unrepentant" .)