On the off chance, accepting second note in additional amount (8)
I believe the answer is:
increase
'note in additional amount' is the definition.
'increase' can be an answer for 'amount' (increase is a kind of amount). I am not certain of the 'note in additional' bit.
'on the off chance accepting second' is the wordplay.
'on the off chance' becomes 'incase' (I've seen this before).
'accepting' is an insertion indicator (inserted letters are accepted).
'second' becomes 're' (prefix meaning second in eg review, re-education).
'incase' placed around 're' is 'INCREASE'.
Can you help me to learn more?
(Other definitions for increase that I've seen before include "Grow greater" , "rise in wages, perhaps" , "'Augment, expand (8)'" , "step up" , "Profit" .)