Ka dib markii uu ciyaaray ciyaaraha barafka ee ciyaaraha yar yar ee Ontario Hockey League (OHL) ee Windsor Spitfires, Gleason waxaa lagu soo qaatay wareegga koowaad, 23aad ee guud ahaan 2001 NHL Entry Draft
waxaa goostay Ottawa Senators. Isaga oo aan awoodin inuu heshiis la gaaro qandaraaska Senators, Gleason waxaa markii dambe lagu beddelay Los Angeles Kings si loogu beddelo weeraryahanka Bryan Smolinski bishii Maarso 11, 2003.