I don’t think much of that Republican oaf (4)
I believe the answer is:
boor
'oaf' is the definition.
(I've seen this before)
'i don't think much of that republican' is the wordplay.
'i don't think much of that' becomes 'boo' ('boo' is an expression of disapproval).
'republican' becomes 'R' (abbreviation in US politics).
'boo'+'r'='BOOR'
(Other definitions for boor that I've seen before include "Coarse, ill-mannered person" , "Rough, bad-mannered person" , "Rude, uncultured type" , "Crude uncouth person" , "Rude uncouth person" .)