You should have the option to hide the notes section if a ticket is closed. That way customer’s cannot add a note that could potentially go missed. This could potentially also have the Service Centre’s contact details and or a link back to re-log a ticket if it was closed incorrectly.
Adding a note to an already closed ticket could run the risk of it being missed, not processed, re-opened when the ticket was rejected by the line manager or by a teams / group approval and is not advisable. It was rejected for a reason and the customer should be logging a new request with the details required.