In 2010, Peak was a key member of the Gaffney team that went on to the SCHSL 4A state championship. As a sophomore in 2012, Peak scored 22 points, including 2 free throws with 7 seconds left in regulation, before fouling out to lead Gaffney in the 58–55 overtime victory over Lexington in the SCHSL 4A state championship. In the 2013 CPL playoffs February 15 finals contest Peak tallied 13 points in a 60–56 overtime Public League Championship game victory against Morgan Park High School by a Whitney Young team that also included Jahlil Okafor. He committed to Georgetown on July 2, 2013, choosing the Hoyas over offers from Florida State and South Carolina. At the time of his commitment, he was the 54th and 82nd ranked player in the Class of 2014, according to ESPN.com and Rivals.com, respectively. Peak closed out his high school career with a 49-point performance against Irmo High School in the third round of the SCHSL playoffs. Peak was named 2014 South Carolina Mr. Basketball.
On November 15, 2014 against St. Francis, Peak started and established the Georgetown record for most points (23) in a freshman debut when he hit all 9 of his field goals and posted the most points by a Georgetown freshman in a game during the John Thompson III era. The 9-for-9 shooting performance was the best performance of the season by a Big East Conference player. Peak developed a reputation for his defensive versatility as a freshman. Following the 2014–15 Big East season, he was selected to the Big East Conference All-Rookie Team.
On January 19, 2016, in an 81–72 upset of the #5-ranked Xavier Musketeers, Peak posted a 13-point, 10-rebound double-double off the bench. On March 6, Peak scored a career-high 31 points against #3-ranked (and eventual national champion) Villanova.
Peak entered his junior season as a 2016–17 preseason All-Big East honorable mention selection. He was a leader in many of Georgetown's wins that year. In a November 21 victory over #13/12 Oregon at the Maui Invitational Tournament, Peak scored 17 points including the free throws to seal the win with 2.7 seconds left. On January 25 against the #16/16 Creighton Bluejays, Peak contributed a game-high 20 points, giving him 1,000 in his Hoya career, in an upset. Three days later he posted a game-high 22 points in another upset over #11/11 Butler. Peak followed those performances up by scoring a game-high 26 points, including the final 5 points of the game in a January 31 76–73 win over DePaul.
Following the season, ESPN's Jeff Goodman reported on March 21, 2017 that Peak would declare himself eligible for the 2017 NBA draft. Peak had almost declared for the 2016 NBA draft and had a family to support at the time of his decision. The Georgetown basketball program was in a state of turmoil, with a top recruit leaving the program and head coach John Thompson III was fired 2 days later. On April 30, 2017, Jeff Goodman of ESPN reported that he was named as an alternate to the NBA Draft Combine.
On June 23, 2017, Peak was signed as an undrafted free agent by the Houston Rockets to a 2017 NBA Summer League contract.
On June 18, 2015 Peak was announced as a member of the 12-man 2015 USA Basketball Men's U19 World Championship Team for the 2015 FIBA Under-19 World Championship. The team won the gold medal against Croatia.
Born in Gaffney, South Carolina, he is the son of Lafayette and Lynette Peak and has one brother, Jermaine Adams.