The U.S. presidential election is a quadrennial event, something that happens every four years. And because the word also means "lasting four years," you can say that the newly-elected President will serve a quadrennial term.
While the "happening every four years" meaning is more common, you can use the word quadrennial in both ways. You might describe your high school years, ninth to twelfth grade, as a quadrennial, while also referring to your favorite quadrennial sporting event, Olympic figure skating. This word is from the Latin quadri-, "four," and -ennial, from annus, "year."