Varhélyi joined the senior national team at the age of eighteen. Her first competition with them was the 2009 European Championships in which Hungary took the fourth place. At the 2013 World Fencing Championships at home in Budapest 110th-ranked Várhelyi fenced Germany's Sibylle Klemm in the first round; she reversed a 6–9 lead and won 15–13. She then edged out Spain's Sandra Marcos and prevailed over France's Béline Boulay to reach the quarter-finals, a career best as of 2014. She was stopped by World No.1 Olha Kharlan, who eventually won the gold medal. She finished the season No.28, her best ranking as of 2014.