Leaves half the side pieces (7)
I believe the answer is:
departs
'leaves' is the definition.
(departing is a kind of leaving)
'half the side pieces' is the wordplay.
'half' suggests halving the letters.
'pieces' becomes 'parts' ('part' can be a synonym of 'piece'**).
'side' halved is 'de'.
'de'+'parts'='DEPARTS'
(Other definitions for departs that I've seen before include "Does runner" , "Goes away" , "Goes, leaves" , "Quits" .)