Look outside, Peter! (4)
I believe the answer is:
peer
'look' is the definition.
(peering is a kind of looking)
'outside peter' is the wordplay.
'outside' suggests removing the centre (I've seen 'outside of' mean this).
'peter' with its centre taken out is 'PEER'.
(Other definitions for peer that I've seen before include "Fellow" , "in another place?" , "Look hard through narrowed eyes" , "Aristocrat" , "Noble; look intently" .)