Set off on outing, regretting leaving ten behind (7)
I believe the answer is:
trigger
'set off' is the definition.
(synonyms)
I can't explain the rest of the clue.
Can you help me to learn more?
(Other definitions for trigger that I've seen before include "Lever on gun" , "Releasing device" , "Roy Rogers' horse" , "Start" , "Activating device" .)