Prevail upon or induce (8)
I believe the answer is:
persuade
I believe this is a double definition.
'prevail upon' is the first definition.
(I've seen this before)
'induce' is the second definition.
(I know that persuade is a more specific form of induce)
(Other definitions for persuade that I've seen before include "Convince. cajole" , "'Coax, inveigle (8)'" , "Induce or convince to do something" , "influence" , "Urge successfully" .)