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 give a lot more credence to this answer).
'after' means one lot of letters go next to another.
'ts' after 'car' is 'CARTS'.
'that' is the 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" .)