Republican party winning everything in race (6)
I believe the answer is:
gallop
'race' is the definition.
(thesaurus)
'republican party winning everything' is the wordplay.
'republican party' becomes 'GOP' (the Grand Old Party, nickname for US Republicans).
'winning' indicates putting letters inside (some letters win or obtain others).
'everything' becomes 'all' (all things).
'gop' going around 'all' is 'GALLOP'.
'in' is the link.
(Other definitions for gallop that I've seen before include "Horse's gait" , "'At GPO, all can go at this pace (6)'" , "Log pal in at this pace" , "Animal's fast pace" , "Fast gait of a horse" .)