Wear down eastern evil-doer (5)
I believe the answer is:
erode
'wear down' is the definition.
(to erode is to wear down or decay)
'eastern evil-doer' is the wordplay.
'eastern' becomes 'e'.
'evil' is an anagram indicator.
'doer' is an anagram of 'rode'.
'e'+'rode'='ERODE'
(Other definitions for erode that I've seen before include "Gradually destroy" , "'Deteriorate, wear away (5)'" , "go to pieces!" , "Gradually wear away" , "Wear away with weather" .)