A central promise of President-elect Donald Trump’s foreign policy is that he will forge a working partnership with Russia, turning an old adversary into an ally in combating terrorist networks overseas and other global threats that bedeviled President Barack Obama.

Now, that vision of an enduring detente will be sorely tested when Mr. Trump takes office Jan. 20 amid one of the worst diplomatic crises between the two nations since the end of the Cold War.

Much...