Run musical show outside of Trieste (7)
I believe the answer is:
operate
'run' is the definition.
('operate' can be a synonym of 'run')
'musical show outside of trieste' is the wordplay.
'musical show' becomes 'opera'.
'outside of' says to hollow out the word (remove centre letters).
'trieste' with its centre removed is 'te'.
'opera'+'te'='OPERATE'
(Other definitions for operate that I've seen before include "Control, run, a mcahine say" , "Control, run, a machine say" , "(Of machine) function" , "Make to work" , "Act in a theatre" .)