Only if you meet the volume thresholds, which vary by country - e.g. for sales to Ireland you must register and pay VAT if your sales are over EUR 35k / year, but in Germany its 100k.
https://www.avalara.com/vatlive/en/vat-news/eu-2021-one-stop...
> At the heart of the 2021 e-commerce EU VAT reboot is the introduction of the One-Stop-Shop (‘OSS’) single EU VAT return and the withdrawal of the Distance Selling thresholds. [...] Non-EU sellers may also apply to use the OSS regime, and just need to nominate any single EU state to register and file in.