2010-11: Leon Bristedt played for Nacka HK in suburban Stockholm — skating for the club's U18 team — and played for Stockholm 1 in the TV-Pucken tournament for high school players. In 28 games for Nacka HK he scored 9 goals with 24 assists and 56 penalty minutes. He scored 1 goal with 3 assists and 6 penalty minutes in eight games as Stockholm 1 won the TV-Pucken championship. Bristedt scored 5 goals with 2 assists and 12 penalty minutes in 11 games for Sweden's U16 team.
2011-12: Bristedt moved from Nacka HK to Linkoping, one of the top clubs in Sweden. He made his debut in Sweden's U20 SuperElit league as a 16-year-old and played for Sweden's U17 team at the 2012 World Hockey Challenge. He scored 4 goals with 1 assist and was -2 in 10 regular season SuperElit games and had no points nor penalties in his only playoff contest. Bristedt scored 18 goals with 11 assists and was +11 with 66 penalty minutes in 31 games with Linkoping's U18 team and scored 1 goal with 1 assist and 2 penalty minutes in three playoff games. He led all players at the WHC with 7 goals in six games and had 1 assist with 10 penalty minutes as Sweden captured a gold medal.
2012-13: Bristedt played in 36 games for Linkoping in his first full SuperElit league season and skated for Sweden's U18 team at the 2012 Ivan Hlinka Memorial and 2013 U18 World Junior Championship tournaments. He scored 9 goals with 12 assists and was +8 with 49 penalty minutes in 31 regular season games for Linkoping and had 3 assists and 2 penalty minutes in five playoff games. Bristedt had 3 assists and was -2 with 6 penalty minutes in five games at the Ivan Hlinka tournament. In five games at the WJC in Sochi he scored 3 goals with 1 assist and had an even plus/minus. Bristedt was ranked 68th amongst European skaters in Central Scouting's final rankings prior to the 2013 NHL Draft but was not selected.
2013-14: Bristedt skated with Linkoping's U20 team to maintain his NCAA eligibility rather than joining the club's SHL team and in November 2013 he committed to playing college hockey at the University of Minnesota in 2014-15. Bristedt led the SuperElit league with 60 points in 43 games. He scored 32 goals, sharing the league lead with MODO's Victor Olofsson, and was +22 with 28 assists and 91 penalty minutes. In four games with Sweden's U19 team he scored 4 goals with 1 assist and was +4 with 4 penalty minutes. Bristedt was ranked 24th amongst European prospects in Central Scouting's final rankings prior to the 2014 NHL Draft.