Because I’ve seen this come up a few times on Twitter now, I thought it might be helpful to make a note of it here…
Because we’re now a Third Country (with the sun gloriously shining on our
faeces faces), you’ll need to re-register with any single EU member state’s own VAT MOSS system, and you’ll then be covered for selling across the EU.
Ireland’s is by far the easiest if you’re from the UK, if only because the interface is in English: https://www.revenue.ie/en/vat/vat-moss/.
You’ll need to use the non-Union registration option (see again, uplands, sunlit).
If you only sell B2B, then you don’t need to register, but you should show “VAT 0% reverse charge mechanism” and their EU VAT number on your invoice.