Rogue put on concert introduced by this person's composition (9)
I believe the answer is:
impromptu
'composition' is the definition.
(impromptu is a kind of musical composition)
'rogue put on concert introduced by this person's' is the wordplay.
'rogue' indicates anagramming the letters (letters go rogue).
'on' is a charade indicator (letters next to each other).
'concert' becomes 'prom' (abbreviation for promenade concert).
'introduced by' is a charade indicator (letters next to each other).
'this person's' becomes 'I'm' (('I am' - 'this person' means the crossword setter).
'put' with letters rearranged gives 'ptu'.
'ptu' after 'prom' is 'promptu'.
'promptu' put after 'im' is 'IMPROMPTU'.
(Other definitions for impromptu that I've seen before include "On the spur of the moment" , "Unplanned; unrehearsed" , "Offhand" , "Without rehearsal or preparation" , "Unplanned; instrumental piece" .)