Look back, and carry on (4)
I believe the answer is:
keep
'carry on' is the definition.
(thesaurus)
'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' in reverse letter order is 'KEEP'.
'and' acts as a link.
(Other definitions for keep that I've seen before include "Conserve" , "Board and lodgings, perhaps" , "strong position" , "Retain; part of castle" , "Main tower within the walls of a castle" .)