With NATO members on Tuesday agreeing to punt on picking a new secretary-general for NATO, Britons are wondering whether their special American partner, President Biden, has reconnected with his Irish roots at the expense of London’s candidate to lead the military alliance. 

Britain’s attempt to get its defense minister, Ben Wallace, installed as the new NATO secretary-general officially ended Tuesday, when the term of current chief, Jens Soltenberg, was extended for another year. Mr. Wallace’s chances, though, were widely seen as doomed following Prime Minister Sunak’s White House visit in early June. 

Mr. Biden now plans to stop at London for meetings with King Charles and Mr. Sunak on his way to the July 11-12 NATO summit at Vilnius, Lithuania. The British press, which has accused the American president of blocking Mr. Wallace’s candidacy due to his past service in Northern Ireland, may be looking to pounce. 

Mr. Stoltenberg, a former Norwegian premier, has held the top NATO post since 2014. He was scheduled to depart in September before receiving the nod for another year at the helm. The fourth such extension of Mr. Stoltenberg’s term indicates the inability of the alliance’s 31 members to coalesce around a new leader. NATO’s decisions must be approved by its entire membership. 

Mr. Sunak, who had been an enthusiastic supporter of Mr. Wallace’s candidacy to lead NATO, praised Mr. Stoltenberg on Tuesday. “Under @jensstoltenberg’s leadership, NATO has evolved to meet new threats, continued to protect our people and has been steadfast in support of Ukraine,” the premier tweeted. “Looking forward to continuing that work together, Jens. 

The buzz on the eve of Mr. Sunak’s June 8 trip to the White House was that the freshly minted premier would lobby his host to back Mr. Wallace’s candidacy to lead NATO. Indeed, during a White House press conference, Mr. Biden was asked about it. Without mentioning Mr. Wallace by name, Mr. Biden acknowledged that Britain has a “very qualified candidate” for the post.

Asked if the time had come for Britain to lead the alliance, Mr. Biden said, “It may be. That remains to be seen.” He then stressed that America cannot make such decisions on its own: “We’re going to have to get a consensus within NATO.”

This week, though, much of Fleet Street reported on claims that the real reason for Mr. Biden’s cagey answer was personal. As one British newspaper, the Daily Mail, reported this week, “allies of the defense minister” told the press that the American president “thwarted Ben Wallace’s bid to head NATO partly because he served as a British soldier in Northern Ireland.” 

Several London newspapers cited an unnamed ally of Mr. Wallace, who said that Mr. Biden “wears his southern Irish roots on his sleeve and he will be well aware Ben served in the British Army during the Troubles.” Mr. Biden is “hardly particularly pro-British either, so we suspect it was one of the reasons why the President failed to throw his weight behind his candidature,” the source added. 

After initially expressing enthusiasm for the top NATO spot, Mr. Wallace told the Economist last week that “it’s not going to happen,” and that there are “a lot of unresolved issues in NATO.” 

Several European members of NATO may have resented Mr. Wallace’s candidacy following Britain’s Brexit, as they believe a European Union member must lead the organization. Some Europeans also argued that the alliance’s chief must be a former head of state. Others pushed the notion that the time has come for a woman to lead NATO. 

Mr. Biden may have agreed to push a woman as candidate, as he seemed to support Prime Minister Frederiksen of Denmark after meeting her last month. Ms. Frederiksen, though, dropped out of the race shortly afterward, as did the EU’s commissioner, Ursula von der Leyen.

The default choice, then, was to extend Mr. Stoltenberg’s term until October 2024. “With his steady leadership, experience, and judgment, Secretary General Stoltenberg has brought our Alliance through the most significant challenges in European security since World War II,” Mr. Biden said in a statement Tuesday. “Today, our Alliance is stronger, more united and purposeful than it has ever been.”   

Mr. Stoltenberg indeed has grown on the job and steered NATO with a steady hand through its most challenging period in decades. Changing the military alliance’s leadership in the midst of the most consequential recent battle on the continent could be hazardous. Perhaps such considerations were behind the decision to kick the  can that is the NATO leadership battle down the road. 

Yet, if instead affirmative action and the desire to promote gender rights are involved, NATO could well end up damaged. Meanwhile, Mr. Biden may need to do some damage control at London. All other considerations aside, America and Britain are the most reliable members of the military alliance. A rift between them would only harm NATO.