Be at odds with Republican getting into fancy ideas, e.g. (8)
I believe the answer is:
disagree
'be at odds' is the definition.
(I've seen this in another clue)
'republican getting into fancy ideas e g' is the wordplay.
'republican' becomes 'R' (abbreviation in US politics).
'getting into' means one lot of letters goes inside another.
'fancy' indicates an anagram.
'ideas'+'e'+'g'='ideaseg'
'ideaseg' with letters rearranged gives 'disagee'.
'r' put within 'disagee' is 'DISAGREE'.
'with' acts as a link.
(Other definitions for disagree that I've seen before include "Dire ages (anag.)" , "Contradict" , "Quarrel" , "Have a conflicting opinion" , "Differ, object" .)