Advantage, getting chief to begin (4,5)
I believe the answer is:
head start
'advantage' is the definition.
(head start is a kind of advantage)
'chief to begin' is the wordplay.
'chief' becomes 'head' ('head' can be a synonym of 'chief').
'to begin' becomes 'start' ('start' can be a synonym of 'begin').
'head'+'start'='HEAD START'
'getting' is the link.
(Other definitions for head start that I've seen before include "advantage, initially" , "Substantial initial advantage" , "'The advantage of beginning ahead of others (4,5)'" , "It improves the chances of success!" , "An early advantage for the star ad" .)