To set off, cartoon cat crosses river (7)
I believe the answer is:
trigger
'to set off' is the definition.
(synonyms)
'cartoon cat crosses river' is the wordplay.
'cartoon cat' becomes 'Tigger' (tiger-like character from Winnie the Pooh stories).
'crosses' indicates putting letters inside.
'river' becomes 'r' (abbreviation for river).
'tigger' going around 'r' is 'TRIGGER'.
(Other definitions for trigger that I've seen before include "One pulled to fire" , "make things happen" , "Part of gun" , "Releasing device" , "Cause (device) to operate" .)