Sharpe attended Piscataway Township High School in Piscataway, New Jersey. He was a two-star recruit by Rivals.com and committed to the University of Massachusetts (UMass) to play college football. 
Sharpe played in 11 games and made eight starts as a freshman at UMass in 2012. He had 20 receptions for 206 yards. Sharpe led the team with 61 receptions for 680 yards and four touchdowns in 2013 and 85 receptions for 1,281 yards and seven touchdowns in 2014.    As a senior in 2015, he broke UMass records for career receptions and receiving yards, finishing the season with 111 receptions for 1,319 yards and five touchdowns.    
|College Stats||Receiving||Rushing||Kick Returns||Punt Returns|
|Ht||Wt||Arm length||Hand size||40‑yd dash||10-yd split||20-yd split||20‑ss||3‑cone||Vert jump||Broad||BP|
| 6 ft 2 in |
| 194 lb |
| 32 1 ⁄ 4 in |
| 8 3 ⁄ 8 in |
|4.55 s|| 33.5 in |
| 9 ft 6 in |
|All values from NFL Combine.|
On May 9, 2016, the Titans signed Sharpe to a four-year, $2.61 million contract with a signing bonus of $274,884.
Throughout training camp, Sharpe competed with Andre Johnson, Dorial Green-Beckham, and Kendall Wright for a starting wide receiver position. He was named one of the starting wide receivers, opposite Rishard Matthews, going into the regular season. Sharpe made his professional regular season debut and first career start in the Titans season opener against the Minnesota Vikings. He finished the 16-25 loss with seven receptions for 76 receiving yards. On November 13, 2016, he caught three passes for 68 receiving yards and scored his first career touchdown on a 33-yard touchdown pass from Marcus Mariota. He contributed to the Titans 47-25 rout the Green Bay Packers. The next game, Sharpe caught four passes for 68 receiving yards and caught a 34-yard touchdown pass in a 17-24 loss to the Indianapolis Colts.  He went on to finish his rookie season with 41 receptions, 522 yards, and 2 touchdowns.
On September 2, 2017, Sharpe was placed on injured reserve with a foot injury.
On May 10, 2017, Sharpe and fellow teammate Sebastian Tretola were named as defendants in a federal civil lawsuit that alleges the teammates were at a Nashville bar watching the 2017 NFL Draft. Dante R. Satterfield, the plaintiff in the lawsuit, claims he told Sharpe he'd probably lose playing time as a result of the Titan's selecting wide receiver Corey Davis in the first round. The report alleges Sharpe responded by challenging him to a fight in a back alley and was accompanied by Tretola as a lookout. Satterfield claims he was knocked unconscious for 12 hours, suffered a concussion, and facial fractures from the incident and is suing for $500,000 in damages.