Having exchanged parts, withdraw stage curtain (8)
I believe the answer is:
backdrop
'stage curtain' is the definition.
(a backdrop hangs behind actors)
I can't explain the remainder of the clue.
(Other definitions for backdrop that I've seen before include "Theatrical scenery" , "Wider view" , "Setting for a scene" , "Scenery hung at the rear of a stage" , "Painted rear stage cloth" .)