Seoul responded smartly to Britain’s vote to leave the European Union, with top diplomat Yun Byung-se saying Friday he wanted a bilateral free-trade agreement with London. This is more evidence of South Korean trade leadership in Asia, and a model for the U.S. and others.

Though South Korea’s economy has suffered in recent years from China’s slowdown and a dearth of domestic entrepreneurship, growth would be far weaker without the healthy trade ties Seoul has secured via agreements with the U.S. (signed in 2007), the EU (2010)...