Side's superiority (4)
I believe the answer is:
edge
This clue is a double definition.
'side's' is the first definition.
(edge is a kind of side)
'superiority' is the second definition.
('edge' can be a synonym of 'superiority')
(Other definitions for edge that I've seen before include "small advantage" , "Creep" , "on which one is ill at ease?" , "Perimeter" , "Cutting side as of knife, or margin" .)