The European Council’s incoming president, Donald Tusk, is a seasoned politician who has been prime minister of Poland since 2007, one of the longest-serving national leaders on the body that steers the 28-nation European Union.

At 57 years of age, Mr. Tusk has been active in domestic politics for most of his adult life, playing a minor role in the anticommunist Solidarity labor movement that helped usher in democracy in Poland in…