Vehicles carrying favourite rugs (7)
I believe the answer is:
carpets
'rugs' is the definition.
('carpet' can be a synonym of 'rug')
'vehicles carrying favourite' is the wordplay.
'vehicles' becomes 'cars' (car is a kind of vehicle).
'carrying' means one lot of letters goes inside another.
'favourite' becomes 'pet' ('pet' can be a synonym of 'favourite').
'cars' placed around 'pet' is 'CARPETS'.
(Other definitions for carpets that I've seen before include "Reprimands (informal)" , "Floor-coverings" .)