Fighter’s strangely impartial over a Republican Yankee (12)
I believe the answer is:
paramilitary
'fighter's' is the definition.
(member of a paramilitary organization)
'strangely impartial over a republican yankee' is the wordplay.
'strangely' indicates anagramming the letters.
'over' says to put letters next to each other (in a down clue, some letters go over others).
'republican' becomes 'R' (abbreviation in US politics).
'yankee' becomes 'Y' (phonetic alphabet: alpha, bravo, charlie etc.).
'impartial' is an anagram of 'paramilit'.
'paramilit'+'a'+'r'+'y'='PARAMILITARY'
(Other definitions for paramilitary that I've seen before include "Member of armed anti-government organisation" , "(Member) of organised armed civilian combat group" .)