Continue to make peer serve (9)
I believe the answer is:
persevere
'continue' is the definition.
(persevering is a kind of continuing)
'make peer serve' is the wordplay.
'make' indicates anagramming the letters.
'peer'+'serve'='peerserve'
'peerserve' is an anagram of 'PERSEVERE'.
'to' acts as a link.
(Other definitions for persevere that I've seen before include "Be unwilling to stop" , "Serve peer (anag.)" , "Continue (against odds)" , "Soldier on" , "Carry on regardless" .)