Press is way out, covering physical exertions by Democrat and follower (8)
I believe the answer is:
expedite
'press' is the definition.
(thesaurus)
I can't explain the remainder of the clue.
Can you help me to learn more?
(Other definitions for expedite that I've seen before include "Make happen faster" , "Hasten, facilitate" , "Cause to be done more quickly" , "Hasten (something)" , "Hasten progress" .)