Manage, at a later time, to set off in pursuit (3,5)
I believe the answer is:
run after
'set off in pursuit' is the definition.
(to run after someone is to pursue them)
'manage at a later time' is the wordplay.
'manage' becomes 'run' (both can mean to organise).
'at a later time' becomes 'after' (after a period of time).
'run'+'after'='RUN AFTER'
'to' is the link.
(Other definitions for run after that I've seen before include "Chase" , "Pursue - on the trot?" .)