Survives final son (5)
I believe the answer is:
lasts
'survives' is the definition.
('last' can be a synonym of 'survive')
'final son' is the wordplay.
'final' becomes 'last' ('last' can be a synonym of 'final').
'son' becomes 's'.
'last'+'s'='LASTS'
(Other definitions for lasts that I've seen before include "carries on" , "Keeps on" , "Cobblers' tools" , "Holds out" , "Goes on" .)