Team figure skating, as an Olympic event, started at the 2014 Winter Games in Sochi, Russia.

In this format, countries field teams made up of skaters from all four main disciplines (men’s singles, women’s singles, pairs, and ice dance), and their individual scores are combined into one overall team result.

If you were asking more broadly about “team-style” figure skating (not just the Olympics), trophy-based club team standings existed as early as the first half of the 20th century, but the modern international team event really solidified with the ISU World Team Trophy, first held in 2009 in Tokyo.

TL;DR:

  • Olympic team figure skating debut: 2014 Sochi Winter Olympics.
  • First ISU World Team Trophy (major modern team event): 2009, Tokyo.

Information gathered from public forums or data available on the internet and portrayed here.