2010-11: Robert Hagg played for Tierps HK men's team in lower Swedish hockey as a 15-year-old, skating in 30 games for the East coast club, and played for MODO's U18 and U16 teams. He scored 2 goals with 9 assists and had 30 penalty minutes for Tierps HK. He was scoreless with 2 penalty minutes in two U18 games for MODO and scored 2 goals with 13 assists and 26 penalty minutes in eight games for MODO U16. Playing for Uppland in the TV-Pucken tournament for Swedish high school players Hagg led all defensemen with 4 goals with 5 assists in eight games.
2011-12: Hagg moved to MODO for the full season, spending most of the year with the U20 squad, and represented Sweden in the 2011 U19 World Junior A Challenge and 2012 U17 World Hockey Challenge tournaments in Canada. In 52 games for MODO U20, including eight playoff games, he scored 5 goals with 14 assists and was plus-11 with 48 penalty minutes. He played six games for MODO U18; scoring 1 goal with 4 assists and was minus-one. Hagg was scoreless with 4 penalty minutes at the WJAC and scored 2 goals with 4 assists and had 16 penalty minutes in six games at the WHC.
2012-13: Hagg split the season between MODO's Elitserien and U20 Super Elit league teams – playing in 27 games with the men's team and being named the top Super Elit defenseman. He played for Sweden in the 2013 U20 and U18 World Junior Championship tournaments, serving as an assistant captain on the U18 squad. Hagg had 1 assist and was minus-three, averaging 7:46 minutes of ice time, in Elitserien regular season play. Seventh place MODO played Farjestad in the playoffs but Hagg did not see any ice time in the five-game series. Hagg scored 11 goals with 13 assists in 28 games with MODO's U20 team during the regular season and played for both the MODO U20 and U18 teams in the playoffs (both of which won silver medals). He also won a silver medal with Sweden at the U20 WJC scoring 1 goal with 1 assist and was minus-one in five games. Sweden's U18 team reached the quarterfinals and in five games Hagg scored 1 goal with 3 assists and was plus-one with 12 penalty minutes. Hagg was ranked eighth amongst European skaters in Central Scouitng's final rankings prior to the 2013 NHL Draft.