Gradually get closer - that will give you the advantage (4)
I believe the answer is:
edge
'the advantage' is the definition.
(having the edge is having an advantage)
I can't explain the rest of the clue.
Can you help me to learn more?
(Other definitions for edge that I've seen before include "Side, brink" , "Border or cutting side of knife" , "Guitarist with U2" , "Steal" , "Skirt" .)