Tarpey joined Collingwood in mid-1988 from Oakleigh District, where he played with his brother Howard, after recovering from ACL Reconstruction back in 1986[1] Tarpey didn't play many senior games for Collingwood and only scored one goal, but he did contribute at the reserves level, winning the Joseph Wren Memorial Trophy in 1989.
After leaving Collingwood, at the end of 1991, he joined Sandringham in the Victorian Football League (VFL), winning with them the 1992 premiership.
[2] He had been drafted by the Richmond Football Club in the 1992 Mid-Season Draft, but opted to stay with Sandringham and did not play any senior games for Richmond.
[3][4] Tarpey joined Smithton as a captain coach in 1993.
[5] In 1996, Tarpey played for Clayton in the Southern Football League (SFL).