Transport favourite rug (6)
I believe the answer is:
carpet
'rug' is the definition.
(I know that rug can be written as carpet)
'transport favourite' is the wordplay.
'transport' becomes 'car' (car is a method of transport).
'favourite' becomes 'pet' (synonyms).
'car'+'pet'='CARPET'
(Other definitions for carpet that I've seen before include "Floor cover" , "On the ......- getting a ticking-off" , "What may deaden sound in room" , "Be on this floor covering to be reprimanded" , "Soft floor covering, red for VIPs" .)