Composer's intro mostly sassy, regularly (7)
I believe the answer is:
debussy
'composer's' is the definition.
(Claude Debussy)
'intro mostly sassy regularly' is the wordplay.
'intro' becomes 'debut'.
'mostly' means to remove the last letter.
'regularly' indicates alternate letters (regularly take one letter, leave next etc.).
The alternating letters of 'sassy' are 'ssy'.
'debut' with its final letter removed is 'debu'.
'debu'+'ssy'='DEBUSSY'
(Other definitions for debussy that I've seen before include "Claude -, C. nineteen-twenty French composer" , "Claude, impressionist composer" , "Claude -, Fr. composer" , "Note-writer" , "Clair de Lune composer" .)