De Niro's furiously chasing naughty child inside (10)
I believe the answer is:
imprisoned
'inside' is the definition.
(thesaurus)
'de niro's furiously chasing naughty child' is the wordplay.
'furiously' indicates anagramming the letters (the letters move around energetically or furiously).
'chasing' is a charade indicator (letters next to each other) (some letters chase after others).
'naughty child' becomes 'imp' (informal term for a misbehaving child).
'de'+'niros'='deniros'
'deniros' is an anagram of 'risoned'.
'risoned' put after 'imp' is 'IMPRISONED'.
(Other definitions for imprisoned that I've seen before include "in jail" , "Locked up" , "behind bars" , "Put away" .)