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, President Emmanuel Macron of France, who is 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.