Radical mistake one's found in empty threat (9)
I believe the answer is:
terrorist
'radical' is the definition.
(terrorist is a kind of radical)
'mistake one's found in empty threat' is the wordplay.
'mistake' becomes 'error' ('error' can be a synonym of 'mistake'**).
'one's' becomes 'is' (roman numeral).
'found in' means one lot of letters goes inside another.
'empty' suggests removing the centre.
'threat' with its centre taken out is 'tt'.
'error'+'is'='erroris'
'erroris' inserted within 'tt' is 'TERRORIST'.
(Other definitions for terrorist that I've seen before include "who breeds fear" , "Guerrilla" , "killer" , "Person who uses violence for political purposes, such as member of Al Qaeda" , "One who uses violence as a means to an end" .)