Vehicles that start up after a car! (5)
I believe the answer is:
carts
'vehicles' is the definition.
(cart is a kind of vehicle)
'start up after a car' is the wordplay.
'start up' becomes 'ts' (I am not sure about this - if you are sure you should believe this answer much more).
'after' means one lot of letters go next to another.
'ts' after 'car' is 'CARTS'.
'that' acts as a link.
Can you help me to learn more?
(Other definitions for carts that I've seen before include "Two-wheeled drawn vehicles" , "Wheeled vehicles that can be pushed or pulled" .)