Reportedly kill for winter transport (6)
I believe the answer is:
sleigh
'winter transport' is the definition.
(I've seen this before)
'reportedly kill' is the wordplay.
'reportedly' shows a homophone (sound like).
'kill' becomes 'slay' (slaying is a kind of killing).
'slay' is a homophone of 'SLEIGH'.
'for' is the link.
(Other definitions for sleigh that I've seen before include "Vehicle with runners; sounds like" , "Santa's vehicle" , "transport in snowbound area" , "transport (with bells on!)" , "ice, you say, in the Rockies?" .)