Set off from assignation outside school (8)
I believe the answer is:
detonate
'set off' is the definition.
(synonyms)
'assignation outside school' is the wordplay.
'assignation' becomes 'date' (I've seen this before).
'outside' means one lot of letters goes inside another.
'school' becomes 'eton' (famous UK public school).
'date' going around 'eton' is 'DETONATE'.
'from' acts as a link.
(Other definitions for detonate that I've seen before include "Set off explosive device" , "Discharge" , "Trigger" , "Start 15 [EXPLOSION]" , "go off with a bang" .)