Before request, take off a little winter covering (3,4)
I believe the answer is:
ski mask
'winter covering' is the definition.
(skiing is a winter sport)
'before request take off a little' is the wordplay.
'before' says to put letters next to each other.
'request' becomes 'ask' (to ask is to request something).
'take off a little' becomes 'skim' (skim can mean to take a small amount off).
'ask' put after 'skim' is 'SKI MASK'.
(Other definitions for ski mask that I've seen before include "bank robber's protection" , "protective winter gear" .)