Pushy people have promotion (4)
I believe the answer is:
hype
'promotion' is the definition.
(I know that hype is a type of promotion)
'pushy people have' is the wordplay.
'have' indicates a hidden word.
'HYPE' is hidden in the letters of 'pushy people'.
(Other definitions for hype that I've seen before include "Puffery" , "Advert" , "Exaggerated advocacy" , "used by pusher?" , "Artificially induced excitement" .)