Set off for 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 inside 'date' is 'DETONATE'.
'for' acts as a link.
(Other definitions for detonate that I've seen before include "Blow up, explode" , "Cause to explode" , "Discharge" , "Start 15 [EXPLOSION]" , "go off with a bang" .)