One pumping round into Republican? Au contraire! (5)
I believe the answer is:
heart
'one pumping' is the definition.
(hearts pump blood)
'round into republican? au contraire' is the wordplay.
I cannot quite see how this works, but
'republican?' could be 'r' (abbreviation) and 'r' is found within the answer.
'round' could be 'heat' (stage of a competition) and 'heat' is present in the leftover letters.
No letters remain.
This explanation may well be incorrect...
(Other definitions for heart that I've seen before include "Not a club" , "Central part" , "Playing card - pity" , "the name of a prison in Midlothian!" , "Centre; core" .)