What a Republican achieved must inspire reactionary (7)
I believe the answer is:
diehard
'reactionary' is the definition.
(thesaurus)
'what a republican achieved must inspire' is the wordplay.
'what' becomes 'eh' (sound used to ask 'what?' or 'pardon?').
'republican' becomes 'R' (abbreviation in US politics).
'achieved' becomes 'did' (to do something is to achieve it).
'must inspire' means one lot of letters goes inside another (inserted letters get inspired or absorbed).
'eh'+'a'+'r'='ehar'
'ehar' placed inside 'did' is 'DIEHARD'.
(Other definitions for diehard that I've seen before include "One to resist change" , "Backer of a losing cause" , "Person who resists change" , "One strongly opposed to change" , "Obstinately conservative" .)