Run as Communist? (4)
I believe the answer is:
trot
I believe this is a double definition.
'run' is the first definition.
(trotting is a kind of running)
'communist' is the second definition.
(short for Trotskyist)
'as' is the link.
(Other definitions for trot that I've seen before include "Left wing" , "Go at steady pace" , "Move quite fast" , "leftie" , "Horse's gait - extreme leftist" .)