Headless golf club giving slight advantage (4)
I believe the answer is:
edge
'slight advantage' is the definition.
(I've seen this before)
'headless golf club' is the wordplay.
'headless' means to remove the first letter.
'golf club' becomes 'wedge' (type of golf club).
'wedge' with its first letter removed is 'EDGE'.
'giving' acts as a link.
(Other definitions for edge that I've seen before include "Keenness" , "Create borders" , "Snick - boundary" , "Skirt" , "incisiveness" .)