Shelf life begins with slight advantage (5)
I believe the answer is:
ledge
'shelf' is the definition.
('ledge' can be a synonym of 'shelf')
'life begins with slight advantage' is the wordplay.
'begins with' says to take the initial letters (I've seen 'begin with' mean this).
'slight advantage' becomes 'edge' (I've seen this before).
The initial letter of 'life' is 'l'.
'l'+'edge'='LEDGE'
(Other definitions for ledge that I've seen before include "Surface under e.g. window" , "A step" , "Sill" , "Projecting shelf, horizontal projection" , "Narrow projection or shelf" .)