Clements attended Canevin Catholic High School in Pittsburgh, Pennsylvania. Clements was a four-year letterman in both football and basketball. He was also offered a basketball scholarship at North Carolina, but decided to play football instead. He is the only athlete in Canevin history to have his jersey retired.
Clements was the starting quarterback for the Notre Dame football team from 1972 to 1974 and led the team to a national championship in 1973. In the December 31, 1973, Sugar Bowl matchup against Alabama, Clements had a 36-yard square-out completion to tight end Robin Weber on 3rd and 9 from his own end zone with 2:00 left to secure a 24-23 victory. In 1974, Clements finished fourth in the voting for the Heisman Trophy and was voted a first-team All-American.
During his time with Ottawa, Clements shared the passing duties with Condredge Holloway, from 1975 to 1977 as the quarterback getting the most playing time. In 1978, their stats were comparable, except for Holloway throwing only two interceptions to 12 by Clements.
Clements continued his career with the Saskatchewan Roughriders in 1979, but did not fare well, throwing only two touchdowns to 11 interceptions and being replaced by Danny Sanders. However, a trade to the Hamilton Tiger-Cats quickly rejuvenated Clements, and he led the CFL in passing yards with 2,803, the last to do so with less than 3,000 yards. In 1980, Clements was briefly on the roster of the NFL's Kansas City Chiefs, coached by former Montreal Alouettes head coach Marv Levy, but was the third-string quarterback for a team that stressed the running game. In 1981, Clements returned to the Tiger-Cats and threw for 4,536 yards. He improved his numbers the next season with 4,706 yards. In 1983, Clements was traded from Hamilton to the Winnipeg Blue Bombers for long-time Blue Bomber quarterback Dieter Brock. The next year, those two teams, Hamilton and Winnipeg, faced each other in the Grey Cup. Clements led the Bombers to their first Grey Cup victory since 1962. In 1986, he set a new completion percentage record with 67.5, 173 out of 256. Clements finished his playing career with Winnipeg in 1987 and was also named the league's Most Outstanding Player. He finished his CFL career with over 39,000 passing yards, 252 passing touchdowns, and a 60.35 completion percentage. In 2005, for the 75th anniversary of the Winnipeg Blue Bombers, Clements was selected one of the Bombers 20 all-time great players. In addition, in November 2006, he was voted one of the CFL's Top 50 players (#47) of the league's modern era by Canadian sports network TSN.
In 2004 and 2005 Clements served as offensive coordinator for the Buffalo Bills, but was released by the team after a front-office shakeup in which Marv Levy, his coach with the Chiefs in 1980, assumed the position of general manager and ultimately installed Dick Jauron as the team's new head coach. Upon the hiring of Mike McCarthy to be the head coach of the Green Bay Packers on January 11, 2006, the Packers parted ways with several assistant coaches, and McCarthy later interviewed NFL Europe head coach Steve Logan and Clements, settling on Clements on January 28, 2006.
During Clements time as the quarterbacks coach with the Packers, he has worked with starting quarterbacks: Brett Favre, Aaron Rodgers, and Matt Flynn. In 2007, Favre statistically had one of his best seasons with the Packers, taking them to the NFC Championship game. Clements is also credited for assisting in the development of one of the game's elite quarterbacks in Aaron Rodgers, as the only player in NFL history to throw for 4,000+ yards during his first two years as a starting quarterback in 2008 and 2009, and winning Super Bowl XLV and Super Bowl Most Valuable Player Award in Rodgers' third year as a starting quarterback in 2010. In Week 17 of the 2011 season, after the Packers went 14-1, McCarthy chose to deactivate Rodgers to keep him healthy for the playoffs and start backup quarterback, Matt Flynn, on January 1, 2012 at Lambeau Field vs. the Detroit Lions, Flynn's second start in his career. Throughout the game, Clements worked with Flynn on the sidelines, showing him what to look for in the photos from the previous offensive series. Flynn had a record-setting performance, throwing for 480 yards and 6 touchdowns, both single game records for the Packers. On February 12, 2015, Clements role was elevated to assistant head coach with respective play-calling responsibilities. On January 26, 2017, McCarthy announced Clements' contract had expired and he would move on to pursue other opportunities.
On January 22, 2019, Clements was hired as passing game coordinator/quarterbacks coach for the Arizona Cardinals on the staff of new head coach Kliff Kingsbury after being out of the NFL the past two years. Clements was hired as the primary offensive assistant because no offensive coordinator on the staff was added, with Kingsbury calling plays and doing other coordinator-type duties.
While still in the CFL, Clements received his Juris Doctor degree magna cum laude from Notre Dame Law School in 1986. Upon the completion of his playing career, he practiced law in Chicago for five years at the law firm Bell, Boyd & Lloyd (now K&L Gates).