As the European General Data Protection Regulation applies to all EU member states, nothing stands in the way of data processing within the European Union. However, if data is processed outside the European Union in so-called "third countries", you must check whether there is an adequate level of data protection in the country so that personal data is also well protected there.
The GDPR regulates the "transfers of personal data to third countries or international organisations" in Chapter 5 (Articles 44 to 50 GDPR).
A transfer to a third country outside the EU is only permitted if the European Commission has recognised the third country as having an adequate level of protection.
From the European Commission's perspective, Norway, Liechtenstein and Iceland are on an equal footing with the EU member states. The European Commission has also recognised Andorra, Argentina, Canada (commercial organisations), the Faroe Islands, Guernsey, Israel, the Isle of Man, Japan, Jersey, New Zealand, the Republic of Korea, Switzerland, the United Kingdom under the General Data Protection Regulation and the LED, the United States (commercial organisations participating in the EU-US data protection framework) and Uruguay as providing adequate protection.
A list of the current countries can be found on the EU Commission's website: https://commission.europa.eu/law/law-topic/data-protection/international-dimension-data-protection/adequacy-decisions_en
If a transfer of personal data to countries not included in this list is planned, the only option is to use the so-called "EU standard contractual clauses" or other sufficient guarantees. The standard contractual clauses are a model contract issued by the European Commission. With these contracts, the service provider in the third country undertakes to comply with European data protection standards. If these model contracts are used, personal data can be transferred to third countries without further authorisation from the supervisory authorities.
A template of the EU standard contractual clauses can be found on the website of the EU Commission: https://commission.europa.eu/law/law-topic/data-protection/international-dimension-data-protection/standard-contractual-clauses-scc_en