Going down without right piloting (7)
I believe the answer is:
driving
'piloting' is the definition.
'going down without right' is the wordplay.
'going down' becomes 'diving' (diving is a kind of going down).
'without' means one lot of letters goes inside another ('without' can be similar in meaning to 'outside').
'right' becomes 'r' (common abbreviation).
'diving' placed around 'r' is 'DRIVING'.
(Other definitions for driving that I've seen before include "Urging along" , "(and 2) Document permitting one to operate vehicle on the roads" , "Behind the wheel" , "(Of rain) forceful" , "Compelling; directing" .)