Regretting having to destroy a note (5)
I believe the answer is:
ruing
'regretting' is the definition.
('rue' can be a synonym of 'regret')
'to destroy a note' is the wordplay.
'to destroy' becomes 'ruin' (synonyms).
'a note' becomes 'g' (musical note).
'ruin'+'g'='RUING'
'having' is the link.
(Other definitions for ruing that I've seen before include "Feeling sorry for" , "Feeling bad" , "Having second thoughts" , "feeling remorse" , "Bitterly regretting" .)