Set off for appointment outside school (8)
I believe the answer is:
detonate
'set off' is the definition.
('detonate' can be a synonym of 'set off')
'appointment outside school' is the wordplay.
'appointment' becomes 'date' ('date' can be a synonym of 'appointment').
'outside' is an insertion indicator.
'school' becomes 'eton' (famous UK public school).
'date' enclosing 'eton' is 'DETONATE'.
'for' is the link.
(Other definitions for detonate that I've seen before include "Blow up, explode" , "Set off explosive device" , "Trigger" , "Discharge" , "Cause to explode" .)