Gémesi won a bronze medal in the 2003 Cadet World Championships in Trapani. In 2013, he took part in his first World Championships, which were held that year in Hungary. He reached the quarter-finals, where he was defeated by team-mate and reigning Olympic champion Áron Szilágyi. The next season, he climbed his first World Cup podium with a silver medal in Madrid. On his first participation to European Championships, he made his way to the semi-finals. He was defeated by reigning World champion Veniamin Reshetnikov and came away with a bronze medal. In the World Championships in Kazan, he was eliminated in the first round by team Olympic champion Oh Eun-seok. In the team event, Hungary were defeated by Italy in the semi-finals, but prevailed over Russia to take the bronze medal.
