First reminder
A polite overdue invoice email
Send this a few days after the due date. Most late invoices are buried, not refused. The note should be easy to answer.
Wait until the invoice is actually late. A reminder on the due date reads as impatience. Three to seven days is enough space for a payment that was already scheduled.
Say what it is: the invoice number, the amount, what the work was, and the due date. Then give them a way out that is still a reply. Either the payment is on the way, or they need the invoice again.
Leave out apologies for asking. You did the work. Also leave out a story about your cash flow. The invoice is the reason.
One note is enough for the first week. If they answer with a date, put that date on your calendar and don’t write again before it. If the date passes, that is the second ask.