Undrafted, Zámorský played as a youth with PSG Zlín of the Czech Extraliga. In his third professional season in 2013–14 with Championship winning Zlin, he was selected as the Czech Extraliga's Best Defenseman. On May 5, 2014, he initially signed a two-year contract as a free agent with Espoo Blues of the Finnish Liiga.[1]
After appearing in his first senior international tournament at the 2014 World Championships in which he finished second amongst Czech defenseman in scoring, Zámorský caught NHL attention and used his NHL 'out clause' with the Blues to sign a two-year entry-level contract with the New York Rangers on June 11, 2014.[2] Zámorský was returned to the Blues on loan for the first year of his contract in the 2014–15 season.
In his first North American season in 2015–16, Zámorský attended the Rangers training camp and on September 23, 2015, was assigned to their American Hockey League affiliate, the Hartford Wolf Pack to begin the year. He contributed with a goal and assist in 10 games, before he opted for a return to Europe and was placed on unconditional waivers, terminating his contract with the New York Rangers on November 17, 2015.[3] On November 23, 2015, he returned to Örebro HK of the SHL on a two-year deal.[4]