In 1992 he played in West Coast's Premiership team and earned All-Australian selection as well as West Coast's best and fairest award. In 1994 he played in the side's second premiership team and won the Norm Smith Medal for best on ground.
He was selected in the 1996 Team of the Decade and the 2006 Team 20 for the Eagles. In 2001 he was made co-captain with Ben Cousins, but retired later that season. Kemp suffered numerous concussions during his career, including one resulting from a savage hit from Mark Ricciuto, and his career was ultimately shortened somewhat by the effects of these numerous concussions.
Kemp was an outstanding midfielder who surprisingly never polled well in the Brownlow Medal count, polling only 53 career votes, with a season best of 13 in 2000. A reason put forward for this is that Kemp was not a flashy ball carrier type player. Rather, on gaining possession of the ball, would quickly and effectively dispose of it to a teammate.
He was also particularly good playing in the wet, rarely fumbling the greasy ball. He enjoyed a successful career after he was drafted at number 117 in the 1989 draft. The lateness of his selection in the draft is frequently highlighted to argue that late draft picks can still prove themselves to be star players.