Succeeded in leaving to survive (5)
I believe the answer is:
exist
'survive' is the definition.
('exist' can be a synonym of 'survive')
'succeeded in leaving' is the wordplay.
'succeeded' becomes 's' (genealogical abbreviation).
'in' is an insertion indicator.
'leaving' becomes 'exit' (exit is a kind of leaving).
's' placed into 'exit' is 'EXIST'.
'to' is the link.
(Other definitions for exist that I've seen before include "Have objective reality" , "Get a life!" , "Survive" , "quick!" , "Have being or continue living" .)