Old horse-drawn vehicle carrying a whip (4)
I believe the answer is:
flay
'whip' is the definition.
(I've seen this before)
'old horse-drawn vehicle carrying a' is the wordplay.
'old horse-drawn vehicle' becomes 'fly' (type of horse-drawn carriage).
'carrying' indicates putting letters inside.
'fly' enclosing 'a' is 'FLAY'.
(Other definitions for flay that I've seen before include "Strip the skin from (a carcass)" , "Slate" , "Whip so as to remove skin" , "Savagely criticise; skin" , "Strip skin from (a body)" .)