Prime Minister Keir Starmer of Britain will barely get his feet under the desk in 10 Downing Street before he flies to Washington this coming week to attend a NATO summit. A week after that, he will play host to 50 European leaders at a security meeting at Blenheim Palace, the birthplace of Winston Churchill.

It’s a crash course in global statecraft for Mr. Starmer, Britain’s first Labour prime minister in 14 years. But it will also give him the chance to project an image of Britain that is uncharacteristic in the post-Brexit era: a stable, conventional, center-left country amid a churning tide of politically unsettled allies.

In Washington, Mr. Starmer will encounter President Biden, who is resisting calls to abandon his race for re-election because of age-related decline. He will meet with President Emmanuel Macron, whose attempt to fend off the far right in France appears to have backfired, and with Chancellor Olaf Scholz of Germany, whose coalition has been weakened by the advance of the hard right in European Parliament elections.

Mr. Starmer’s success with Labour may raise hopes among some that Britain’s embrace of a center-left party could be replicated in France and the United States. But it is equally plausible that Britain could be a harbinger of something else: an anti-incumbent revolt and simmering populism, embodied in Britain by the insurgent Reform party, that could play out elsewhere. That was the case in 2016, when voters backed the Brexit referendum six months before the United States elected Donald J. Trump.

Britain’s shift to Labour, analysts pointed out, was not about ideology so much as about fatigue with a Conservative government and distrust of political institutions in general. That same fatigue exists in France, under an unpopular centrist president, and in the United States, under an aging Democratic one.