Continue to look back (4)
I believe the answer is:
keep
'continue' is the definition.
(I know that continue can be written as keep)
'look back' is the wordplay.
'look' becomes 'peek' (peek can mean to look at quickly).
'back' says the letters should be written in reverse.
'peek' backwards is 'KEEP'.
'to' is the link.
(Other definitions for keep that I've seen before include "Look after" , "Save" , "run" , "honour" , "Retain; part of castle" .)