Chap in vehicle, getting stiff (7)
I believe the answer is:
cadaver
'stiff' is the definition.
(I know that stiff can be written as cadaver)
'chap in vehicle' is the wordplay.
'chap' becomes 'dave' (man's name).
'in' means one lot of letters goes inside another.
'vehicle' becomes 'car' (car is a kind of vehicle).
'dave' placed into 'car' is 'CADAVER'.
'getting' is the link.
(Other definitions for cadaver that I've seen before include "Human body dissected by medical students" , "Human corpse" , "A kind of corpse" , "Stiff" , "Remains of a human" .)