Left-winger to make brisk progress (4)
I believe the answer is:
trot
I believe this clue is a double definition.
'left-winger' is the first definition.
(short for Trotskyite)
'make brisk progress' is the second definition.
(to trot is to move at a brisk pace)
'to' acts as a link.
(Other definitions for trot that I've seen before include "Run (like a horse)" , "Clip (horse)" , "Jog along" , "Steady gentle run" , "Move like a horse" .)