Steal the limelight from leading coach (7)
I believe the answer is:
upstage
'steal the limelight' is the definition.
'leading coach' is the wordplay.
'leading' becomes 'up' ('up' can be similar in meaning to 'leading').
'coach' becomes 'stage' (stagecoach**).
'up'+'stage'='UPSTAGE'
'from' is the link.
(Other definitions for upstage that I've seen before include "Outshine" , "moved away from the audience" , "Take the limelight from" , "dwarf?" , "Divert attention from another as actor may" .)