Clark was born in Sioux Falls, South Dakota. He graduated from Twin River Valley High School in Bode, Iowa, where he was a multi-sport star. He earned four letters in football, basketball, and track and 30 letters in baseball. As a high schooler, he earned honorable mention all-conference honors in football and was second team all-conference as a sophomore. As a junior, Clark was named his team's most valuable player and a first-team all-conference and honorable mention all-state selection after recording 140 tackles. He was team captain and MVP again as a senior, recording 160 tackles, and earned first-team all-conference and second-team all-state honors.
Clark attended the University of Iowa, where he played for the Iowa Hawkeyes football team from 1999 to 2002. He did not see action during the 1999 season, but he finally saw the field in 2000. He played on special teams and made six tackles during the season as a linebacker. Prior to the 2001 season, the Iowa coaching staff decided to move Clark to the tight end position.
Clark started 10 games at tight end for Iowa in 2001, catching 38 passes for 539 yards and four touchdowns on the season. He also played special teams, recovering an on-side kick to clinch a win against Penn State and recording five tackles on the year. Clark was named honorable mention All-Big Ten Conference.
After being granted a scholarship for 2002, Clark started all 13 games as he helped lead Iowa to its first undefeated conference season in 80 years. Clark was the Big Ten Offensive Player of the Week against Purdue, when he caught three passes for 116 yards and two touchdowns. His first touchdown came in the third quarter, when he broke a Purdue tackle and raced 95 yards for a touchdown. It was the longest pass play in Kinnick Stadium history and the second longest in school history. Clark's second touchdown came with 1:07 left in the game. With the Hawkeyes trailing, 28-24, Clark caught a seven-yard pass on fourth and goal from quarterback Brad Banks to give Iowa a 31-28 win.
Clark was the 2002 recipient of the John Mackey Award which is presented to the most outstanding tight end in college football, a first-team All-Big Ten selection, and a unanimous first-team All-American. He won the Kenny Yana Award at the end of the 2002 season as well, as he helped lead Iowa to the Big Ten title and an 11-2 record. Although he had one more year of eligibility remaining, Clark decided to enter the 2003 NFL Draft. He left Iowa with 1,281 career receiving yards in just two years at the tight end position.
Clark was chosen in the first round of the 2003 NFL draft by the Indianapolis Colts with the 24th pick. When drafted, the Colts called Clark a "perfect fit" for their system, eventually replacing Marcus Pollard and Ken Dilger at the position. He started 10 games as a rookie and had 340 receiving yards before suffering a broken leg against the New England Patriots. He started 15 games in 2004 and had 423 yards receiving with five touchdown receptions.
Clark started 15 games in 2005 and caught 37 passes for 488 yards and four touchdowns. He started in 11 games in the 2006 season before suffering a knee injury in the November 26 home game against the Philadelphia Eagles. He returned for the playoffs and played very well leading up to the Colts' first Super Bowl berth since moving to Indianapolis. In the Colts' three playoff games, he caught a total of 17 passes for 281 yards as a member of the 2006 Super Bowl Champion Indianapolis Colts. In the 29-17 victory over the Chicago Bears, he caught four passes for 36 yards and rushed the ball once for a one-yard gain. In 15 starts in 2007 season, Clark had 58 receptions for 616 yards, shattering John Mackey Colts record for receptions for a tight end (55) and touchdowns (11).
On February 19, 2008, the Colts placed the franchise tag on Clark. The next day, the Colts signed him to a six-year contract extension, with his salary averaging $4.5 million per year ($41 million in total), making him the highest paid tight end in the NFL.
On December 28, 2008, Clark broke the Colts' franchise record, held by Hall of Famer John Mackey, for yards in a season by a tight end (848). On September 21, 2009, Clark had career high 183 receiving yards and a touchdown in just seven receptions at the Monday Night Football match up against Miami Dolphins, this is also the fourth highest receiving yards ever for a Tight End in NFL history. On November 8, 2009 against the Houston Texans Clark caught 14 balls; a career-high for him. He was named AFC Offensive Player-of-the-Week because of his performance against Houston. On January 3, 2010 against the Buffalo Bills, Clark caught his 100th reception of the season, the second tight end to do so in NFL history. He ended the 2009 season with 100 catches for 1,106 yards and 10 touchdowns.
On October 17, 2010, Clark sustained a wrist injury playing the Washington Redskins and was put on injured reserve on Friday, October 22, 2010, after season-ending wrist surgery. He completed the season with 37 catches for 347 yards and three touchdowns.
Clark's surgically repaired wrist would again hinder his production in the 2011 regular season, limiting him to 34 receptions for 357 yards and two touchdowns in only 11 games. This was also the first season Clark played without quarterback Peyton Manning, who missed the entire season rehabbing from offseason neck surgery. Clark was released on March 7, 2012.
Clark signed a one-year contract with the Tampa Bay Buccaneers on May 21, 2012. He finished the season with 47 receptions for 435 yards and 4 touchdowns.
On August 13, 2013, Clark signed a one-year contract with the Baltimore Ravens. He finished the season with 31 receptions for 343 yards and 3 touchdowns.
On June 18, 2014, Clark signed a one-day contract with the Colts, so that he could retire as a member of the team.
Clark and his wife, Karen, reside with their two sons in Livermore, Iowa and daughter Hazel. They also hold residence in Zionsville, Indiana.
Clark has guest starred in the CBS hit show Criminal Minds as San Diego Police officer Austin Kent in the episode "The Stranger", fulfilling an acting dream."