Vivaldi wrote a lot of these, anything but priestly at the core (5)
I believe the answer is:
notes
'vivaldi wrote a lot' is the definition.
I can't judge whether this definition defines the answer.
'these anything but priestly at the core' is the wordplay.
'these anything but' becomes 'not' (I've seen this in other clues).
'priestly' becomes 's' (I can't explain this - if you can you should give a lot more credence to this answer).
'at' is a charade indicator (letters next to each other) (I've seen this in other clues).
'the' becomes 'definite article' ('the' is the definite article in English).
'core' indicates the central letters.
The middle of 'definitearticle' is 'e'.
's' after 'e' is 'es'.
'not'+'es'='NOTES'
'of' acts as a link.
Can you help me to learn more?
(Other definitions for notes that I've seen before include "Sees" , "Written comments" , "output from musicians" , "Memoranda" , "Cash" .)