Notoriously surreptitious tirade by convict on the inside (10)
I believe the answer is:
flagrantly
'notoriously' is the definition.
(thesaurus)
'surreptitious tirade by convict on the inside' is the wordplay.
'surreptitious' becomes 'fly' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'tirade' becomes 'rant' (both can mean an angry outburst).
'by' means one lot of letters go next to another.
'convict' becomes 'lag' (slang term for a prisoner).
'on the inside' is an insertion indicator.
'rant' put after 'lag' is 'lagrant'.
'fly' placed around 'lagrant' is 'FLAGRANTLY'.
Can you help me to learn more?
(Other definitions for flagrantly that I've seen before include "in a scandalous way" , "in conspicuous manner" .)