Bright red vehicle belonging to me (7)
I believe the answer is:
carmine
'bright red' is the definition.
(I've seen this before)
'vehicle belonging to me' is the wordplay.
'vehicle' becomes 'car' (car is a kind of vehicle).
'belonging to me' becomes 'mine' (I've seen this before).
'car'+'mine'='CARMINE'
(Other definitions for carmine that I've seen before include "Bright red" , "Vivid red colour" , "Crimson pigment" .)