Terreri dipilih ku New Jersey Devils dina babak kalima (85th sakabéh) tina 1983 NHL Entry Draft
. tapi Anjeunna ngahadiran Providence College ti taun 1982 nepi ka 1986, sarta jadi MVP turnamén posseason Hockey East 1985 sanggeus meunangna 2<unk>1 dina waktu tambahan ganda ngalawan Boston College di Providence Civic Center, sarta jadi MVP tina NCAA Men's Ice Hockey Championship 1985, sanajan éléh 2<unk>1 dina pertandingan jawara ka RPI di Joe Louis Arena.