Female censors upset about international art of public debate (9)
I believe the answer is:
forensics
'art of public debate' is the definition.
(forensic can mean relating to discussions in court)
'female censors upset about international' is the wordplay.
'female' becomes 'f' (common abbreviation).
'upset' is an anagram indicator.
'about' is an insertion indicator.
'international' becomes 'i' (abbreviation eg in IMF).
'f'+'censors'='fcensors'
'fcensors' with letters rearranged gives 'forenscs'.
'forenscs' enclosing 'i' is 'FORENSICS'.
(Other definitions for forensics that I've seen before include "If censors combined in medical studies for legal purposes" , "study of public debate" .)