Alex Insam, whose older sister Evelyn Insam was also active as a ski jumper, started skiing early like her. In August 2011 he made his international debut at the FIS Junior Show Jumping in Hinterzarten . After another junior competition in February, he made his debut in the Alpine Ski Jumping Cup in August 2012 . In October he was used for the first time in the FIS Cup in Einsiedeln, Switzerland, and jumped straight into the points. He did not succeed in this in the Alpine Cup. At the Junior World Championships 2013 in Liberec he reached after a weak 52nd place in the individual competition, the 12th with the team in the team competition. After he did not start in Kranj despite a report, he started at the European Youth Olympic Winter Festival 2013 in Râșnov and jumped to 25th place.
In February 2014 Insam managed to jump into the points twice again when he started again in the FIS Cup in Brattleboro . On January 6, 2015, he also made it into the Alpine Cup points for the first time in Seefeld in Tirol . At the following Junior World Championships in 2015 in Almaty , he reached 15th place in individual jumping. In February 2015 he made his debut in Titisee-Neustadt as part of the Ski Jumping Continental Cup . He stayed in this series until the end of winter 2014/15, but missed the points in all competitions. On July 5, 2015, Insam jumped into the second round of the Kranj mat jumping for the first time in this series and thus won his first Continental Cup points. At the Malinka in Wisła he surprised a little later with the eighth place. He then traveled to Courchevel with the national team to jump in the Ski Jumping Grand Prix . After he still missed the qualification there, he reached the competition in Einsiedeln and finished in 39th place. In Almaty he won Grand Prix points for the first time after jumping to 18th place. With these points, he finally reached 70th place overall.
In September 2015, he was second on the podium for the first time at the Alpencup jumping competition in Hinterzarten. After he reached the points in the Continental Cup twice in Klingenthal in October , he was nominated for the World Cup in November in the same place. After finishing eleventh in his team jumping World Cup debut with the team on November 21, 2015, he missed the qualification for the individual competition the following day. On January 8, 2016, he took part in the qualification for the World Cup in Willingen , but did not make it into the competition again. On January 31, he finished second on a Continental Cup podium for the first time at the Continental Cup in Bischofshofen . He also continued to perform well in the Alpine Cup and two weeks later celebrated two second places there in Planica . On March 3, he took part in the qualification for the World Cup in Wisła, in which he fell on landing, after which he had to be taken to hospital, again as 44th just failed in the competition. After his fall, on the advice of the doctors, he no longer took part in the second competition.
After jumping in the FIS Cup and the Continental Cup in the 2016/17 season , he competed in the World Cup at the Four Hills Tournament in Innsbruck . He missed the points again as 44th. Then he went back to the COC. At the 2017 Junior World Championships in Park City , he won the silver medal in the individual behind Viktor Polášek . In the mixed team competition, he was fifth. At the Nordic World Ski Championships in Lahti he was ranked 45th on the normal hill and 37th on the large hill in the individual competitions. After the World Cup he took part in the newly introduced Raw Air . In the final ski flying of this series in Vikersund , he was 25th to get the first World Cup points of his career. He finished the Raw Air as 26th overall. At the World Cup final in Planica on March 24, 2017, he improved his best World Cup result to 15th place. In the trial run for this competition, he set a new Italian record in ski flying with 232.5 meters .