Carriage factor's looking up (4)
I believe the answer is:
trap
'carriage' is the definition.
(I know that trap is a type of carriage)
'factor's looking up' is the wordplay.
'factor' becomes 'part'.
'looking up' says the letters should be written backwards (in a down clue, letters go up).
'part' reversed gives 'TRAP'.
(Other definitions for trap that I've seen before include "Snare - mouth" , "Catch; two-wheeled carriage" , "Ambush" , "Means of transport (sometime sprung!)" , "that can let an actor down" .)