He played college football at Louisiana State University (LSU), where he won the Jim Thorpe Award as the best defensive back in the country and was recognized as a unanimous All-American.

[6] Claiborne attended Louisiana State University, where he played for coach Les Miles's LSU Tigers football team from 2009 to 2011.

[7][8] After spending his freshman season as a backup in 2009, he started 12 games in 2010 and recorded 37 tackles and a team-leading five interceptions as a sophomore in 2010, and was named a second-team All-Southeastern Conference (SEC) selection.

[14][15][16] By midseason, however, he had drawn the attention of NFL scouts and analysts, having erased concerns his sophomore production resulted from playing opposite of Patrick Peterson.

[24] Claiborne withheld surgery to repair a wrist injury until after he performed at the NFL Combine and LSU's pro day.

[34] Head coach Jason Garrett named Claiborne and Brandon Carr the starting cornerbacks to begin the regular season.

[35] He made his professional regular season debut and first career start in the Dallas Cowboys' season-opener at the New York Giants and recorded four solo tackles during their 24–17 victory.

[36] On October 21, 2012, Claiborne recorded two combined tackles, deflected two passes, and made his first career interception as the Cowboys defeated the Carolina Panthers 19–14 in Week 7.

[37] Claiborne intercepted a pass by Panthers' quarterback Cam Newton, that was originally intended for wide receiver Louis Murphy, during the second quarter.

[43] Claiborne entered training camp slated as a starting cornerback, but sustained numerous injuries that delayed his progress.

[51] Claiborne missed four consecutive games (Weeks 13–16) and explained his rehabilitation was delayed due to the death of his father and birth of his daughter.

[56] Head coach Jason Garrett named Claiborne and Brandon Carr the starting cornerback tandem to begin the regular season after Orlando Scandrick was suspended for the first two games.

[57] On September 21, 2014, Claiborne recorded a season-high three solo tackles, deflected a pass, and made an interception during a 34–31 victory at the St. Louis Rams in Week 3.

[62] Claiborne rehabbed his potential career-threatening injury and progressed better than expected, regaining his previous form and being able to avoid missing time in training camp.

Throughout training camp, Claiborne competed to be a starting cornerback against Brandon Carr, Orlando Scandrick, and Byron Jones.

[63] Head coach Jason Garrett named Claiborne and Brandon Carr the starting cornerbacks to begin the regular season after Orlando Scandrick tore his ACL and MCL during the preseason.

[69] In training camp, while Orlando Scandrick was out recovering from a knee injury, he earned the starting left cornerback position.

[73] There was a fear that the injury could require season-ending surgery,[74] but the team decided to let it to heal on its own and not place Claiborne on the injured reserve list.

[75][76] On March 18, 2017, Claiborne signed a one-year contract with the New York Jets, who were looking to replace veteran Darrelle Revis at cornerback.