Pála Pók started swimming in the Eger and later became a water polo player for the club. He left his hometown in 1952 after which he played for Bp. Vasas, then from 1955 for Bp. Vörös Meteor, between 1957-1958 for Újpesti Dózsa, and then between 1960-1961 for Bp. Spartacus. He was a player on the 1953 champion water polo team of Bp. Vasas. He only played for the Hungarian national team once, at the 1948 London Olympics. Thus, he could call himself an Olympic silver medallist with just one national team match.
Pók graduated from the Faculty of Political Science and Law at the Budapest University. Later he worked in the hospitality industry. His daughter Edina was a national backstroke swimmer.