Student outside university arranged duet to be broadcast (13)
I believe the answer is:
undergraduate
'student' is the definition.
(university student)
'outside university arranged duet to be broadcast' is the wordplay.
'outside' means one lot of letters goes inside another.
'university' becomes 'u' (abbreviation for university).
'to be broadcast' indicates an anagram (letters scattered or cast around).
'arranged'+'duet'='arrangedduet'
'arrangedduet' is an anagram of 'undergradate'.
'u' going into 'undergradate' is 'UNDERGRADUATE'.
(Other definitions for undergraduate that I've seen before include "One studying for a first degree" , "University student yet to take degree" .)