Note delivered after the last month in fall (7)
I believe the answer is:
decline
'month in fall' is the definition.
'decline' can be an answer for 'fall' (synonyms). I'm unsure of the 'month in' bit.
'note delivered after the last' is the wordplay.
'note' becomes 'D' (musical note).
'delivered' becomes 'cline' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'after' is a charade indicator (letters next to each other).
'last' suggests the final letters.
The last letter of 'the' is 'e'.
'cline' put after 'e' is 'ecline'.
'd'+'ecline'='DECLINE'
Can you help me to learn more?
(Other definitions for decline that I've seen before include "Start to fail" , "Refuse; decay" , "Refuse - to go down" , "Say no or lose strength" , "go through cases" .)