Myre started his career in the 1964 playoffs with the QMJHL's Victoriaville Bruins, going 1-1 in two of those games, then 0-1 in one Memorial Cup appearance. In his first full season in Victoriaville in the 1964-65 season, Myre played 21 games and finished up 14-7-0, then going 7-2 in nine playoff appearances, while going 0-3 in the Memorial Cup play-down games. Victoriaville moved to Shawinigan for the 1965-66 season, where Myre would go 38-6-0 in 44 games, then 8-4 in 12 playoff games and 11-4 in 15 Memorial Cup play-down games.
Myre was drafted by the Montreal Canadiens in the 1966 Draft, which was also a year that Myre went to the OHA's Niagara Falls Flyers starting in the 1966-67 season, leading them to a Memorial Cup championship following the 1967-68 season.
Turning pro in 1968-69, Myre played in the Central League for the Houston Apollos, going 24-19-10 in 53 games, then going 0-2 in the playoffs.
The 1969-70 season allowed Myre to play in 15 games for the AHL's Montreal Voyageurs before getting the call-up to the Canadiens, where he would play in 10 games with a 4-3-2 record. Myre stayed in Montreal for the 1970-71 season, playing in 30 games with a 13-11-4 record, but would be relegated to back-up when Ken Dryden made his mark in the league. While the Canadiens won the Stanley Cup that year and even though he qualified to be engraved on the Cup, the team left him off, even though he did receive a ring for his efforts. Myre only played nine games for the Canadiens in the 1971-72 season, going 4-5-0 in his efforts.
The Canadiens left Myre unprotected in the 1972 Expansion Draft, allowing the Atlanta Flames to pick him up. In that 1972-73 season, Myre tallied a 16-25-3 record in 46 games, while he went 11-16-6 in 36 games in the 1973-74 season-- in which he played in the team's first playoff series, going 0-3 in three games. Myre played 40 games in the 1974-75 season, finishing in with a 14-16-10 record; while in the 1975-76 and 1976-77 season, Myre went .500 in both seasons, with a 16-16-4 and 17-17-7 record respectively. Myre would only play nine games for the Flames in the 1977-78 season, going 2-7-0 before being put on the move.
Myre was traded to the St. Louis Blues in December of 1977 and would play 44 games for the Blues, going 11-25-8 in those last games. Myre return with the Blues in the 1978-79 season, going a dismal 9-22-8 in his 39 appearances.
Myre was traded to Philadelphia in June of 1979 and join a tandem with Pete Peeters for the 1979-80 season, with Myre going 18-7-15 that season, a season where he and Peeters had a 35-game unbeaten streak-- a NHL record. It wasn't a great for Myre in the 1980-81 season, as he would go 6-5-4 in 16 games before being on the move again.
The Flyers traded Myre to the Colorado Rockies for cash, in which Myre would play 10 games to end out the year and compile a 3-6-1 record. After the '80-'81 season, Myre played for Team Canada in the World Championships, but would go 2-5-0 in seven games. Myre returned to the Rockies for the 1981-82 season, playing in 24 games, finishing with a 2-17-2 record. Myre would also spend time that year with the Central League's Fort Worth Texans, playing in 10 games with a 4-5-1 record.
Myre signed with the Buffalo Sabres before the 1982-83 season, spending a majority of the season with the AHL's Rochester Americans, going 28-8-5 in 43 games, while playing in five games with Buffalo, going 3-2-0. Myre returned to Rochester for the 1983-84 season, going 19-9-1 in 33 games before hanging up his pads for good.
Post-playing career, Myre went into coaching, being an assistant with the Los Angeles Kings and Detroit Red Wings and then as a goalie coach for the Red Wings and also later as goalie coach with the Florida Panthers. Myre also got into some blogging (before it got hacked) and public speaking. Currently, Myre is working with the Montreal Canadiens in a scouting capacity.
While he had his hand in two big team trophies, he was only recognized for one, then started to bounce around from menial team to menial team-- which could have hurt his mentality in the long-run. He kept to it though and made himself a good life after his playing career was finished.