He also made several appearances for the Michigan State Spartans men's basketball team his freshman year before deciding to focus solely on football.

Sims also participated at Michigan State's Pro Day, along with Le'Veon Bell, William Gholston, Johnny Adams, and five other teammates.

Satisfied with his combine numbers, Sims only participated in positional drills and worked out in front of scouts and representatives from 23 teams, including Pittsburgh Steelers head coach Mike Tomlin.

Analysts gave him positive reviews for his quick and nimble feet while blocking, large frame, soft hands, and breakaway tackle ability.

[5] In the 2013 NFL draft, the Miami Dolphins selected Sims in the fourth round, with the 106th overall pick.

[7] He started his rookie year as the backup tight end on the Miami Dolphins' depth chart, behind veteran Charles Clay.

He finished his second season with 24 receptions, 284 receiving yards and two touchdowns and played in 14 games with two starts.

In the season opener against the Washington Redskins, Sims suffered a severe concussion when hitting his head when diving for a touchdown catch in the end zone.

After colliding with the turf, he remained motionless for a few seconds before regaining consciousness and sitting up, with the aid of Dolphin's trainers.

[11] On October 18, 2015, he returned for the first time since the season-opener and made a season-high four receptions for 33 yards and a touchdown in a victory over the Tennessee Titans.

On January 3, 2016, Sims made three catches for a season-high forty yards in a 20–10 victory over the New England Patriots.

[15] On September 10, in his Bears debut, Sims had two receptions for 31 yards in the 23–17 home loss to the Atlanta Falcons at Soldier Field.