As America’s largest trading partners race toward deals, they are increasingly worried about being hit with future tariffs on their critical industries.Governments around the globe are racing to negotiate trade deals with the United States in order to forestall President Trump’s punishing tariffs, which could kick in on July 9. But the discussions have been slowed because Mr. Trump has threatened to impose more tariffs even if those deals are in place. Mr. Trump announced what he refers to as “reciprocal tariffs” on April 8, which he said were in response to other countries' unfair trading practices. But he agreed...