Robertson played many positions in high school, including option quarterback, running back, cornerback, wide receiver, kicker and punter.

[1] Robertson is one of only four former football players from Stafford High School to play in the NFL, others being Boris Anyama, Adrian Awasom, and Jalen Pitre.

[7][8] Throughout OTA's and training camp, he competed for a roster spot, as a backup linebacker, against James-Michael Johnson, Quinton Spears, Kaluka Maiava, Emmanuel Acho, Ben Jacobs, L. J. Fort, and JoJo Dickson.

[9][10] Head coach Pat Shurmur named Robertson the backup outside linebacker, behind Scott Fujita, Kakula Maiava, and James-Michael Johnson, to begin the regular season.

[11] He had an opportunity to play immediately on defense after rookie Emmanuel Acho was placed on injured reserve due to an undisclosed injury, starting outside linebacker Chris Gocong was placed on IR after tearing his Achilles tendon during camp in August, and the Browns' other starting outside linebacker, Scott Fujita, was suspended for the first three games due to his participation in the New Orleans Saints bounty scandal.

[15] In Week 3, Robertson earned his first career start, in place of Kakula Maiava, and made eight combined tackles during a 24–14 loss to the Buffalo Bills.

[14] On November 18, 2012, Robertson recorded five combined tackles and made his first career sack on quarterback Tony Romo during a 23–20 loss at the Dallas Cowboys in Week 11.

[8] On December 31, 2012, it was reported that the Cleveland Browns' new owner, Jimmy Haslam, fired head coach Pat Shurmur and general manager Tom Heckert, Jr. after they finished fourth in the AFC North with a 5–11 record.

[17] Robertson entered OTA's and training camp in 2013 and competed to be a starting inside linebacker in Ray Horton's base 3-4 defense against James-Michael Johnson.

On October 27, 2013, Robertson recorded a season-high 11 solo tackles and sacked Alex Smith in the Browns' 23–17 loss at the Kansas City Chiefs in Week 8.

[25] Defensive coordinator Jim O'Neil held a competition between Robertson and rookie Christian Kirksey for the job as a starting inside linebacker.

[26] Head coach Mike Pettine named Robertson the starter, along with right inside linebacker Karlos Dansby, to start the regular season.

[35] Head coach Sean Payton named Robertson the backup weakside linebacker, behind Dannell Ellerbe, to start the regular season.

[36][37] He made his New Orleans Saints' regular season debut in their season-opener against the Oakland Raiders and recorded 11 combined tackles (eight solo) and a pass deflection in their 35–34 loss.

[38] The following week, he collected nine combined tackles, broke up a pass, and made his first sack as a Saint on quarterback Trevor Siemian during a 25–23 loss to the Denver Broncos.

[39] On December 4, 2016, Robertson recorded four solo tackles before exiting the Saints' 28–13 loss to the Detroit Lions in three fourth quarter after sustaining an injury.

[44] On October 15, 2017, Robertson made his first start of the season and recorded a season-high 11 combined tackles (four solo), deflected a pass, and sacked Matthew Stafford during a 52–38 victory against the Detroit Lions in Week 6.