Chops up the quince, demonstrating skilful method (9)
I believe the answer is:
technique
'skilful method' is the definition.
(I've seen this before)
'chops up the quince' is the wordplay.
'chops up' indicates an anagram (I've seen 'chopped up' mean this).
'the'+'quince'='thequince'
'thequince' anagrammed gives 'TECHNIQUE'.
'demonstrating' acts as a link.
(Other definitions for technique that I've seen before include "Way of carrying our a task" , "Proficiency" , "Skilled procedure or method" , "Skill" , "See 6" .)