DUBLIN — Canada’s deft young prime minister, Justin Trudeau, was beaten at his own game by his younger, newly elected Irish counterpart, Leo Varadkar, in Dublin on Tuesday.

In advance of this first meeting of two of the three fresh faces of Western politics, speculation had centered on whether Mr. Varadkar, 38, and Mr. Trudeau, 45, could recreate the chemistry between Mr. Trudeau and the third member of their youthful trinity, the French president Emmanuel Macron, 39.

Mr. Trudeau and Mr. Macron hit it off at the Group of 7 summit meeting in May and will be reunited later this week at the Group of 20 summit meeting in Germany.

But Mr. Varadkar’s first photo opportunity with Mr. Trudeau in Dublin showed that in this dance for three, nobody outdoes Mr. Varadkar.

Mr. Trudeau has a penchant for quirky hosiery, and he has previously donned socks honoring “Star Wars” and NATO in public appearances. But a sharp-eyed Irish reporter noticed he wore a subdued pair of gray and white striped socks on Tuesday. Mr. Varadkar bested him with a pair of bright red socks, decorated with Canadian Mounties and maple leaves that paid tribute to his visitor.

At a joint news conference Tuesday, Mr. Varadkar brazenly flashed his footwear at the cameras before presenting his guest with a customized Irish rugby shirt and a pair of green Celtic socks.

But Mr. Trudeau had his own moment to shine. During a demonstration of Ireland’s traditional sport of hurling, he proved remarkably adept at the difficult skill of soloing a sliotar, or bouncing a ball on the end of a flat, narrow hurley stick.

Mr. Varadkar, who attended a private school that favored the somewhat more sedate and genteel sport of field hockey, declined to take up the challenge.

“I’m so not doing that,” he said.

Beyond the pleasantries, the leaders had real business to attend to. They reaffirmed their nations’ support for the Comprehensive Economic and Trade Agreement, a free-trade pact between Canada and the European Union, which must be ratified individually by all 28 members of the bloc.

Like its troubled big brother, the Trans-Atlantic Trade and Investment Partnership between the United States and Europe, the Canadian-Irish trade pact has encountered resistance from environmentalists, trade unionists, farmers and others who fear that provisions allowing private companies to sue governments for lost profit will undermine the power of states to enforce regulations.

While acknowledging that there were problems, both leaders said the agreement would be good for their countries.

“We’ve much more to gain from free trade than to lose,” Mr. Varadkar said.

Both leaders pointed to another common bond their nations shared as the smaller neighbors of the global powers Britain and the United States, which are “taking a different direction from many other countries,” as Mr. Trudeau put it.

That circumstance has given both prime ministers more prominence than they might otherwise have. Mr. Trudeau enjoys the rare political combination of good looks, charisma and pedigree. But as Mr. Varadkar pointed out, it was America’s decision to turn inward that helped Canada to re-emerge as a global player after Mr. Trudeau’s election.

Similarly, Mr. Varadkar came to the world’s attention last month as Ireland’s openly gay, half-Indian, youngest-ever prime minister, but it was Britain’s vote to leave the European Union, known as “Brexit,” that moved his country to more global prominence.

Europe has already stated that Britain must address crucial demands of its Irish member state in Brexit negotiations: no hard border between the Republic of Ireland and British-ruled Northern Ireland, a continuation of the present open travel area between Ireland and the Britain.

For all their parallels, Mr. Trudeau and Mr. Varadkar seem to be on different paths at the moment. Eighteen months into his term, Mr. Trudeau is still enjoying a honeymoon period, leveraging his charm to rise above domestic challenges.

Mr. Varadkar is on his second crisis after less than six weeks as the Irish prime minister.

On Monday, while Mr. Trudeau looked forward to playing geopolitics at the G-20 meeting, Mr. Varadkar was scrambling to deal with a looming parliamentary defeat — which would be embarrassing but not fatal to his government — on a private bill about garbage charges.

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