Artist upset after music award mostly for use of language (7)
I believe the answer is:
grammar
'use of language' is the definition.
(grammatical system of a language)
'artist upset after music award mostly' is the wordplay.
'artist' becomes 'RA' (Royal Academician, member of Royal Academy of Arts).
'upset' says the letters should be written in reverse.
'after' is a charade indicator (letters next to each other).
'music award' becomes 'Grammy' (the Grammys are music awards).
'mostly' means to remove the last letter.
'ra' backwards is 'ar'.
'grammy' with its last letter removed is 'gramm'.
'ar' after 'gramm' is 'GRAMMAR'.
'for' acts as a link.
(Other definitions for grammar that I've seen before include "Basic rules of language" , "Correct usage of words" , "Syntax etc" , "Branch of language study" , "Study of word and sentences" .)