Floor covering in vehicle — a favourite (6)
I believe the answer is:
carpet
'floor covering' is the definition.
(carpet is a kind of floor covering)
'vehicle a favourite' is the wordplay.
'vehicle' becomes 'car' (car is a kind of vehicle).
'a favourite' becomes 'pet' ('pet' can be a synonym of 'favourite').
'car'+'pet'='CARPET'
'in' acts as a link.
(Other definitions for carpet that I've seen before include "The red one is for VIPs" , "Runner perhaps" , "Implied but not stated" , "Reprimand severely" , "Floor-covering" .)