Beat both Republican parties (5)
I believe the answer is:
throb
'beat' is the definition.
(throbbing is a kind of beating)
'both republican parties' is the wordplay.
'republican' becomes 'r' (abbreviation).
'parties' is an anagram indicator (the letters move or party around).
'both'+'r'='bothr'
'bothr' with letters rearranged gives 'THROB'.
(Other definitions for throb that I've seen before include "Have strong or irregular heartbeat" , "Beat rhythmically" , "Broth (anag.)" , "Drum" , "Sound of engines" .)