Jun teamed up with South Korea's second-string pilot Kim Dong-hyun, and won his first international gold medal at the 2013 North American Cup, finishing 0.12 seconds ahead of the Monegasque duo of Patrice Servelle and Sébastien Gattuso.

[3] Although Jun along with Kim earned a spot on the 2013–14 World Cup tour, the duo failed to make an impact like they did in the previous second-tier competitions, finishing 32nd in the overall standings.

[4][5] Jun & Kim flourished after the 2014 Winter Olympics under the leadership of British coach Malcolm "Gomer" Lloyd who vastly improved the South Korean bobsleigh team by implementing customized training methods.

But if anything, their performances gradually deteriorated in the second half of the 2016–17 season when the duo began to use the domestic sled that was manufactured by the Hyundai Motor Company, South Korea's largest automaker.

Jun & Kim opted to miss the two-man competitions at the 2017–18 World Cup season in order to focus on the four-man event at the 2018 Winter Olympics.