Medium goal - to cause harm (4)
I believe the answer is:
maim
'harm' is the definition.
(to maim is to harm or injure)
'medium goal' is the wordplay.
'medium' becomes 'm' (as in UK clothing sizes).
'goal' becomes 'aim' (aim is a kind of goal).
'm'+'aim'='MAIM'
'to cause' is the link.
(Other definitions for maim that I've seen before include "Wound, injure, harm" , "Wound and permanently disfigure" , "Injure and cripple" , "Wound or injure, disable" , "Injure permanently" .)