Conciliate (3,4)
'conciliate' is the definition.
(appeasing is a kind of conciliating)
This is the entire clue.
(Other definitions for appease that I've seen before include "Placate (someone) with concessions" , "Calm, pacify, placate" , "Conciliate" , "Placate (someone) by giving in" , "To behave like Chamberlain" .)
(Other definitions for win over that I've seen before include "Bring round (to idea)" , "Gain the support of" , "Persuade" .)