Terrell is a native of Weymouth, Massachusetts and has two brothers, Royce II and Jordan. He began his high school career at Weymouth High School, where he averaged 11 points a game. He made big strides as a sophomore and posted 16 points per game and helped Weymouth to a Bay State Conference Carey Division title with an 18-4 record. The next season, Terrell transferred to the New Hampton School, where one of his teammates was Noah Vonleh. His time at New Hampton was marred by injuries and he transferred again to Brewster Academy, where he was teammates with Devonte' Graham. During two years at Brewster, Terrell averaged 14.5 points, 5.0 rebounds and 3.0 assists. He guided the team to a New England prep title in 2013 and 2014 and was named the MVP of the tournament. Terrell led Brewster to their third National Prep Championship in 2014. Terrell formed a dangerous backcourt at Brewster, which consisted of two other future NBA players in Devonte' Graham and Donovan Mitchel. Terrell was highly recruited out of high school and accepted a scholarship to Oklahoma State before changing his mind and picking Rhode Island.
College career
Despite posting four consecutive losing seasons before Terrell arrived, the Rams finished 23-10 his freshman year and reached the NIT. He was named to the All-Atlantic 10 Rookie Team. As a sophomore, he averaged 13.6 points per game on a 17-15 team. Terrell's scoring went down somewhat as a junior to 12.6 points per game, but the Rams finished 25-10 and reached the NCAA Tournament. Terrell had a son, Jared Jr. in September 2017. On November 27, Terrell had a career-high 32 points in a 75-74 win over Seton Hall and hit the game-winning layup with 5.2 seconds left. As a senior, he led Rhode Island in scoring with 16.8 points per game. He was named to the First Team All-Atlantic 10 as a senior. Terrell led the Rams to 26-8 record and a NCAA Tournament appearance, where they beat Oklahoma behind 13 points from Terrell. Rhode Island bowed out in the second round to Duke despite Terrell contributing 10 points.
On September 14, 2019, Terrell signed a one-year deal with Hapoel Eilat of the Israeli Premier League. On October 28, 2019, Terrell recorded a season-high 25 points, while shooting 8-of-15 from the field, along with four rebounds in an 87–76 win over Maccabi Haifa. On December 20, 2019, he parted ways with Eilat after appearing in six games due to an injury. On January 7, 2020, Terrell signed with Dnipro of the Ukrainian Basketball SuperLeague for the rest of the season. Terrell was named to the "USA/EU" team of the Ukrainian Basketball SuperLeague All-Star Game.
