Set off to make school in time (8)
I believe the answer is:
detonate
'set off' is the definition.
('detonate' can be a synonym of 'set off')
'school in time' is the wordplay.
'school' becomes 'eton' (famous UK public school).
'in' is an insertion indicator.
'time' becomes 'date' (date is a kind of time**).
'eton' going within 'date' is 'DETONATE'.
'to make' acts as a link.
(Other definitions for detonate that I've seen before include "Trigger" , "let off" , "Cause to explode" , "go off with a bang" , "Blow up, explode" .)