Creep giving lip (4)
I believe the answer is:
edge
I believe this is a double definition.
'creep' is the first definition.
(I've seen this in other clues)
'lip' is the second definition.
(thesaurus)
'giving' is the link.
(Other definitions for edge that I've seen before include "Demarcation" , "Sharp ridge" , "Skirt" , "Advantage (informal)" , "Margin, fringe" .)