Rent part of vaudeville theatre (3)
I believe the answer is:
let
'rent' is the definition.
(thesaurus)
'part of vaudeville theatre' is the wordplay.
'part of' says the answer is hidden in the clue.
'LET' is hidden within 'vaudeville theatre'.
(Other definitions for let that I've seen before include "Permit or rent" , "Allow, don't hinder" , "Allow; rental period" , "Award (a contract)" , "Permitted" .)