How do I raise a debit note to a supplier in Aicountly Billing?

Open Debit note (under Purchases, or from the quick actions) and choose the Supplier first. Their bills are then listed under Against Document, so you can pick the purchase bill the note relates to and the two can be matched later.

Select a Reason: Goods sent back to the supplier, Supplier billed the wrong price, Short delivery, Damaged on arrival, or Something else. For returned goods, add the lines and, if needed, choose where they go under Goods go back into; for a price correction, enter the amount to adjust before tax. Billing leaves the GST and ledger entries to Smart Books, which works them out when you post.

You need the debit note permission in your Billing profile; if the screen says you cannot raise one, ask whoever manages access for your company.