At club level, Márton played for Hungarian side Honvéd, until he was acquired by AEK Athens. His acquisition in the 1985 season was considered a great achievement for AEK but, after two good years, he was released in the winter period of 1987 following a series of poor performances. He was picked up by Panathinaikos, failed to impress in the 1987 or 1988 season and was released in December of 1988.
Esterhazy played for the Hungarian national team between 1980-1988 and took part in the World Cup of 1986, in Mexico. He was capped 29 times and scored 11 goals.
His career in Greece