Awful moans stifled by composer mounting carriage (6-3)
I believe the answer is:
hansom cab
'carriage' is the definition.
(hansom cab is a kind of carriage)
'awful moans stifled by composer mounting' is the wordplay.
'awful' indicates an anagram.
'stifled by' indicates putting letters inside (I've seen this in other clues).
'composer' becomes 'bach' (Johann Sebastian Bach).
'mounting' is a reversal indicator (going up in a down clue).
'bach' in reverse letter order is 'hcab'.
'moans' with letters rearranged gives 'ansom'.
'ansom' put into 'hcab' is 'HANSOM-CAB'.
(Other definitions for hansom cab that I've seen before include "Two-wheeled one-horse carriage" , "Victorian transport - mob has can (anag)" , "Horse-drawn two-wheeler" , "Victorian means of transport" , "In old vehicle" .)