Žarnay studied Pedagogy at the University of Prešov. He worked as a proofreader, editor and teacher.[2]
Žarnay worked as a teacher at Commerce Academy high school on the Polárna street in Košice. He was also the director of the teacher parents association at the school. In 2013 he wrote a public letter to the Prime Minister Robert Fico, stating that the school pays €400 monthly for likely bogus "external legal services".[4] The management of the school refused to clarify the nature of services provided.[5] In response the Minister of Education Peter Pellegrini requested a meeting with Žarnay to discuss his concerns.
Žarnay together with an MP Ján Mičovský filed a lawsuit against the school for wasteful and fraudulent use of public funds.[6] The comptroller of Košice regional administration estimates that over the course of contract being in effect, the school paid a total of €12,000 without to a law firm without apparently receiving any services in return.[7] In 2016, this finding was confirmed also by a central government auditor.[5]
After the contract became public knowledge, it was no longer extended and soon expired.[8] Nonetheless, Žarnay was fired for "organizational reasons" along with a physical education teacher who spoke in his defense.[4][8][9] The dismissal was declared invalid by the appellate court of the Košice region in December 2018.[10] The new school principal subsequently announced that Žarnay, who became an MP in the meantime, was welcome to return to be a teacher after his political career ended if he wished to return.[11]