Run away from mischievous prank, avoiding publicity (6)
I believe the answer is:
escape
'run away' is the definition.
(to run away is to escape from somewhere)
'mischievous prank avoiding publicity' is the wordplay.
'mischievous prank' becomes 'escapade'.
'avoiding' is a deletion indicator.
'publicity' becomes 'ad' (advert).
'escapade' with 'ad' taken away is 'ESCAPE'.
'from' acts as a link.
(Other definitions for escape that I've seen before include "Leak; avoid" , "Gain freedom" , "Outlet" , "Break free from confinement" , "Duck" .)