Winter sport aid's existence briefly revealed in burlesque (3,4)
I believe the answer is:
'winter sport aid's' is the definition.
(aid when skiing)
'existence briefly revealed in burlesque' is the wordplay.
'existence' becomes 'life' (being alive).
'briefly' means to remove the last letter.
'revealed in' indicates putting letters inside.
'burlesque' becomes 'skit' (burlesque can mean a sketch or skit).
'life' with its final letter taken away is 'lif'.
'lif' put within 'skit' is 'SKI-LIFT'.
(Other definitions for ski lift that I've seen before include "Device for carrying winter sports enthusiasts" , "Device for transporting people to top of piste" , "Way to the top" , "one can ride up here" , "Winter sports facility" .)