Kim, a two-time Olympic medalist, was seen on the bleachers near the finish zone at Olympic Sliding Centre in PyeongChang, where the third heat of the men's skeleton event is under way.
Wearing a beanie and a black mask, Kim was seen applauding as Yun crossed the finish line. Yun maintained his lead with a combined time of 2 minutes, 30.53 seconds. She also clapped as Kim Ji-soo, another South Korean skeleton slider, finished his run and stayed in sixth place at 2:32.17.
The world famous figure skating star, who lit the Olympic cauldron at the PyeongChang Winter Games' opening ceremony last week, later left the venue after reporters swarmed around her to take photos and ask questions.
Yun started the day as the top-ranked slider with a time of 1:40.35, setting track and start records at Olympic Sliding Centre. He is looking to become the first Asian to win a medal in an Olympic skeleton competition.
The fourth heat, where only the top 20 sliders can compete, will start at 11:15 a.m.