Returning in flashy car, I propose unauthorised activity (6)
I believe the answer is:
piracy
'activity' is the definition.
(piracy is a kind of activity)
'returning in flashy car i propose unauthorised' is the wordplay.
'returning' shows that the letters should be reversed in order.
'in' indicates a hidden word.
'ycarip' is hidden within 'flashy car i propose unauthorised'.
'ycarip' in reverse letter order is 'PIRACY'.
(Other definitions for piracy that I've seen before include "Robbery on the high seas" , "Robbing of ships at sea" , "theft" , "Crime" , "Illegal copying" .)