Gjesvold first appeared at the European Youth Olympic Winter Festival 2003 in Bled, Slovenia on an international level. He achieved eighth place in the individual and a silver medal in the team competition. A little later, he took part in the Junior World Championships in Sollefteå , where he just missed the podium after finishing 37th in the individual with the team and finished fourth.
On August 23, 2003 he made his debut in the Continental Cup in Trondheim . He was active in this series of competitions until 2006, and in between he also competed in the FIS Cup. He achieved his only podium placement at a summer COC on July 25, 2004 on the Schattenbergschanze in Oberstdorf . In the 2005/06 season he was able to collect points for the first time in winter and achieved his best placement with rank 17.
After Gjesvold jumped his last Continental Cup in August 2006, he competed in the FIS Cup again in Einsiedeln and Notodden in 2007 and 2009 before finally ending his career.