In the 2007–08 season she was age-eligible to compete in Junior competitions, so she competed at the 2007–08 ISU Junior Grand Prix, placing 10th at the event in Tallinn with 98.77 points and 13th at the event in England with 103.89. She then competed at the South Korean Championships at the Junior level, where she came in fifth position.
2008–09 season
In the 2008–09 season, she received two assignments to the 2008–09 ISU Junior Grand Prix. She won the bronze medal at the event in Mexico scoring 117.42 points but finished 13th at her competition in England, earning 106.05. She competed at the South Korean Championships again as a Junior, and won the gold medal with 114.89 points, placing first in both the short program and the free skating. She was selected to compete at the 2009 World Junior Championships, and with 103.69 she finished 22nd overall.
2009–10 season: Vancouver Olympics
In the 2009–10 season, Kwak remained in the ISU Junior Grand Prix and competed in two events. She placed 11th in the first one held in the United States with 106.30 points. She went on to place 11th again with 108.21 at her second event, which took place in Croatia. She was selected to compete at the 2010 Four Continents Championships in Jeonju, South Korea, her first Senior international competition. She placed seventh in the short program and fourth in the free skate to end in sixth position earning 154.71 points. Kwak was also chosen to be a member of the South Korean Olympic Team. Before the Olympics she moved to Toronto, Ontario, Canada, and trained with Brian Orser, the 1984 and 1988 Olympic silver medalist. At the 2010 Winter Olympics, held in Vancouver, British Columbia, Canada, where she placed 13th with 155.53 points. She went on to compete at the 2010 World Championships in Turin, Italy, where she was in 22nd position after getting 120.47 points overall. Her collaboration with Orser ended in August 2010.
2010–11 season
In the 2010–11 season, Kwak moved to the senior ISU Grand Prix. Her assignments in the 2010–11 ISU Grand Prix season were the 2010 Cup of China and the 2010 Skate America. At the 2010 Cup of China, she placed ninth in the short program with 38.83 points and also ninth in the free skate with 75.15. Overall, she placed ninth scoring 113.98 points. At the 2010 Skate America, she came tenth in the short program earning 44.41 points, and eleventh in the free skate with 80.80. She had a total of 125.21 points and finished eleventh. She competed at the 2011 South Korean Championships, where she won the short program with 50.48 points. She placed third in the free skate earning 91.78 and won the bronze medal. She was selected to compete at the 2011 Four Continents and 2011 World Championships. At the 2011 Four Continents Figure Skating Championships she placed 8th in both skates finishing overall in 8th place. At the 2011 World Figure Skating Championships she placed 15th in the ladies qualifying round failing to advance to the short.
2011–12 season
At the 2012 South Korean Championships she placed 8th in the short program falling on two of her jump elements to earn 38.98 points. In the free skate she placed 6th with 84.46 to climb up to 6th overall. Later that year, Kwak competed at the 2012 Four Continents Championships where she placed 10th. She has been selected to compete at the 2012 World Championships and she placed 28th.
