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 justify this - if you can you should believe this answer much more).
'at' means one lot of letters go next to another (I've seen this in other clues).
'the' becomes 'definite article' ('the' is the definite article in English).
'core' says to take the centre.
The central letter of 'definitearticle' is 'e'.
's' after 'e' is 'es'.
'not'+'es'='NOTES'
'of' is the 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" .)