Drive away on hearing brogue, say (4)
I believe the answer is:
shoo
'drive away' is the definition.
(shooing is a kind of driving away)
'hearing brogue say' is the wordplay.
'hearing' shows a homophone (sound like).
'brogue say' becomes 'shoe' (brogue is a kind of shoe).
'shoe' sounds like 'SHOO'.
'on' acts as a link.
(Other definitions for shoo that I've seen before include "Dismiss" , "Exclamation used to chase away animals" , "Sound uttered to make animals go away" , "Get lost!" , "Push off" .)