There is free movement of plants and plant products within the EU, apart from a number of plants from specific genera, which require a valid plant passport to be moved throughout the Member states indicating their freedom from certain regulated Harmful Organisms.
https://www.agriculture.gov.ie/farmingsectors/planthealthtrade/transferringofplantstoirelandfromtheeu/
With regard to the product mentioned, turf related products, this can move freely within the EU, however any exporter to a Third Country would need to clarify the import requirements with the National Plant Protection Organisation (NPPO) of the Importing Country.
The FAO International Plant Protection Convention (IPPC) establishes the International Standards for Phytosanitary Measures, (ISPM 12) on Phytosanitary Certificates. This allows my Departments as the Irish NPPO, following inspection, to issue a Phytosanitary Certificate for the plant products or other regulated articles to attest that the consignment meets the specified the Phytosanitary import requirements, and are in conformity with the requirements of the requirements of the NPPO of the importing country.
https://www.agriculture.gov.ie/media/migration/farmingsectors/planthealthandtrade/QuickGuidePhytocerts141015.pdf
My Department works closely with exporters to facilitate such trade movements.