Hasten, being late, and change in gym (8)
I believe the answer is:
expedite
'hasten' is the definition.
('expedite' can be a synonym of 'hasten')
'late and change in gym' is the wordplay.
'late' becomes 'ex'.
'and' means one lot of letters go next to another.
'change' becomes 'edit' (editing is a kind of changing**).
'in' indicates putting letters inside.
'gym' becomes 'pe'.
'edit' going within 'pe' is 'pedite'.
'ex'+'pedite'='EXPEDITE'
'being' acts as a link.
(Other definitions for expedite that I've seen before include "Hasten progress" , "Rush" , "Push through faster" , "Cause to be done more quickly" , "Speed up progress (of)" .)