Boy has set off and survived (6)
I believe the answer is:
lasted
'survived' is the definition.
('last' can be a synonym of 'survive')
'boy has set off' is the wordplay.
'boy' becomes 'lad' (informal term for boy).
'has' is an insertion indicator.
'off' indicates an anagram.
'set' is an anagram of 'ste'.
'lad' enclosing 'ste' is 'LASTED'.
'and' acts as a link.
(Other definitions for lasted that I've seen before include "Continued for some time, endured" , "Endured, survived" , "Continued, being salted" , "Persisted, endured" , "Kept going" .)