Kammala jumla mai zuwa: New Jersey Devils ne suka fara zabarsa a zagaye na uku, na 63 a gaba ɗaya, a cikin NHL Entry Draft na 1996. Duk da haka ba zai iya zuwa ga wata yarjejeniya tare da Devils ya sake shiga cikin
1998 da aka zaba a zagaye na farko, 20th gaba ɗaya, ta Colorado Avalanche. Bayan ya buga wasanni a WHL tare da Kelowna Rockets, Parker ya fara aikinsa na NHL tare da Avalanche a 1998 kuma ya kasance memba na kungiyar gasar cin kofin Stanley ta 2001.