Composition in this person's concert put off (9)
I believe the answer is:
impromptu
'composition' is the definition.
(I know that impromptu is a type of musical passage)
'this person's concert put off' is the wordplay.
'this person's' becomes 'I'm' ('I am' - 'this person' means the crossword set).
'concert' becomes 'prom' (abbreviation for promenade concert).
'off' is an anagram indicator.
'put' is an anagram of 'ptu'.
'im'+'prom'+'ptu'='IMPROMPTU'
'in' is the link.
(Other definitions for impromptu that I've seen before include "Unplanned; composition" , "Spontaneously, off the cuff" , "Off-the-cuff" , "Unscripted" , "Unplanned; unrehearsed" .)