Elegant, fast lute composition (8)
I believe the answer is:
tasteful
'elegant' is the definition.
(associated in meaning)
'fast lute composition' is the wordplay.
'composition' is an anagram indicator (letters arranged or composed in a different order).
'fast'+'lute'='fastlute'
'fastlute' anagrammed gives 'TASTEFUL'.
(Other definitions for tasteful that I've seen before include "Decorous" , "Refined, not tawdry" , "pleasantly entertaining" , "Let Faust have ability to enjoy good things" , "Aesthetically pleasing" .)