The first step is to confirm the infringement: the use must fall within the scope of your registration, meaning an identical or confusingly similar sign used in Slovakia in connection with identical or similar goods or services.
If the use in question constitutes infringement, the standard first step is sending a cease and desist letter that demands that this party stop infringing. If they do not comply with the C&D, enforcement can escalate to court proceedings, including claims for an injunction, damages, and the surrender or destruction of infringing goods.
For online infringement, platform-specific enforcement is often faster: reporting infringing listings on marketplaces, social media, or app stores, or filing a UDRP complaint through WIPO against an infringing domain. If your Slovak trademark is being infringed, Trama can advise on your enforcement options.