Have a quick look back (4)
I believe the answer is:
keep
'have' is the definition.
(keeping is a kind of having)
'a quick look back' is the wordplay.
'a quick look' becomes 'peek' (I've seen this before).
'back' says the letters should be written in reverse.
'peek' written backwards gives 'KEEP'.
(Other definitions for keep that I've seen before include "Castle tower; cost of maintenance" , "Central tower of castle" , "Board and lodgings, perhaps" , "Save" , "Eg, beef" .)