Work permit 

A third country national has the same rights to the use of employment services as any citizen of the Slovak Republic if:
– they have been granted a work permit and a temporary residence permit for employment purposes,
– they are holders of an EU Blue Card,
– they are an asylum seeker whose entry in the labour market is permitted.

For more information please visit
https://www.upsvr.gov.sk/sluzby-zamestnanosti/zamestnavanie-cudzincov.html?page_id=272197