Not oddly, robust oldie vies to survive (7)
I believe the answer is:
outlive
'survive' is the definition.
(synonyms)
'not oddly robust oldie vies' is the wordplay.
'not oddly' indicates alternate letters (odd letters are removed).
'robust'+'oldie'+'vies'='robustoldievies'
The alternate letters of 'robustoldievies' are 'OUTLIVE'.
'to' is the link.
(Other definitions for outlive that I've seen before include "Go on longer than" , "Survive beyond (another)" , "Die after" , "Survive longer than" , "weather" .)