Second half of Mozart's organ composition is imperious (8)
I believe the answer is:
arrogant
'imperious' is the definition.
(thesaurus)
'second half of mozart's organ composition' is the wordplay.
'second half of' means to take half the letters (the back or second half of the word).
'composition' is an anagram indicator (letters arranged or composed in a different order).
'mozart' halved is 'art'.
'art'+'organ'='artorgan'
'artorgan' with letters rearranged gives 'ARROGANT'.
'is' acts as a link.
(Other definitions for arrogant that I've seen before include "Having an exaggerated sense of one's own importance" , "Haughty - imperious" , "Overbearingly proud" , "Overbearing with exaggerated sense of superiority" , "Proud and contemptuous" .)