Debate fever gripping Republican (5)
I believe the answer is:
argue
'debate' is the definition.
(synonyms)
'fever gripping republican' is the wordplay.
'fever' becomes 'ague' (I've seen this before).
'gripping' is an insertion indicator (inserted letters are gripped).
'republican' becomes 'R' (political abbreviation).
'ague' going around 'r' is 'ARGUE'.
(Other definitions for argue that I've seen before include "Dispute, disagree" , "Bandy words" , "Exchange heated views" , "Reason" , "Discuss, contend" .)