Doctor Who's theatrical performance (4)
I believe the answer is:
'theatrical performance' is the definition.
'doctor who's' is the wordplay.
'doctor' indicates an anagram.
'whos' is an anagram of 'SHOW'.
(Other definitions for show that I've seen before include "Demonstrate - parade" , "Demonstrate; spectacle" , "programme" , "charade" , "Exhibit - present" .)