Fight (for) (3)
'fight for' is the definition.
(thesaurus)
This is all the clue.
(Other definitions for vie that I've seen before include "Jockey" , "Compete for something" , "Eagerly compete" , "I've got to contend" , "Engage in rivalry" .)
(Other definitions for strive that I've seen before include "Contend using rivets" , "Make great efforts" , "Rivets (anag)" , "Make a great effort" , "Vie, contend" .)