Harper grew up in Regina, Saskatchewan playing hockey. He played for Regina's local hockey team, which was sponsored by the Montreal Canadiens. In the 1958 Memorial Cup finals, they lost to the Ottawa-Hull Junior Canadiens, who were led by manager Sam Pollock, coach Scotty Bowman and future stars J.C Tremblay, Gilles Tremblay, Ralph Backstrom, and Bobby Rousseau.
Harper played his first 10 seasons with the Montreal Canadiens. He joined the team in 1962. However, he didn't debut for the team until 1963. While with Montreal, Harper had his greatest success, winning five Stanley Cups between 1963 and 1972.
On October 30, 1963, Harper got into an altercation with Bob Pulford of the Toronto Maple Leafs while sharing the penalty box. As a result, separate penalty boxes for teams were created 10 days later.
Prior to the 1972–73 season, Harper was traded to the Los Angeles Kings, where he anchored a defence that became one of the league's stingiest. Harper was immediately named team captain, a position he held for 3 seasons until his trade to Detroit after the 1974–75 season. In 1973, he was an All-Star. In that game, he made a game-tying goal for the West All-Stars. However, Bobby Schmautz then scored the game-winning goal for the East All-Stars. The Kings made the playoffs twice in his tenure there, but each time got bounced in the first round.
After the 1974–75 season, on June 23, 1975, Harper, along with Dan Maloney, was traded to the Detroit Red Wings as part of the blockbuster trade that sent Hall of Famer Marcel Dionne and Bart Crashley to Los Angeles. Once again, he was named team captain for Detroit. In the 1975–76 season, he erupted for a career high eight goals with the Detroit Red Wings. After 4 solid seasons for a struggling Red Wings team, he played his final two seasons for the St. Louis Blues and Colorado Rockies, where he played into his 40s. He retired in 1981, at the age of 41.
In 19 seasons in the league, Harper finished with only 254 points. For his career, he finished with 35 goals, 221 assists, 1,362 penalty minutes, and a plus/minus total of +169 (this statistic did not become official until the 1967–68 season, Harper's 6th in the league).
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