Hasten the progress of (8)
I believe the answer is:
'hasten the progress of' is the definition.
(I've seen this before)
This is all the clue.
(Other definitions for expedite that I've seen before include "Cause to be done more quickly" , "Hurry" , "Cause (something) to happen earlier" , "Hasten (something)" , "Hasten progress" .)