Mrs. Clinton’s signature initiative as America’s top diplomat is what has become known as the administration’s “pivot to Asia,” a strengthening of United States strategic, security and economic ties in the Asia-Pacific region. It is a policy Mr. Obama advanced with his three-country trip that began Saturday and included two nations never before visited by an American president, Myanmar and Cambodia.

Image Credit... The New York Times

Now as the president prepares to begin his second term, the secretary is stepping down, bone weary, according to aides, and ready for an extended rest after nearly a million miles of globe-trotting. She has waxed about the days not far off when she can relax, read a book and even travel just for pleasure. But many on Air Force One these last few days, not least the president himself, expect her to be back after a rest, making a bid to succeed him in 2016 and redefining their relationship once again.

As the last day of the trip arrived on Tuesday morning, Mrs. Clinton reflected briefly. “It’s been great,” she told reporters who stopped her in a hotel before heading out to summit meetings. “It’s been bittersweet, nostalgic, all the things you would expect.”Mr. Obama, too, has seemed to focus on the journey’s nature of finality, making a point of praising Mrs. Clinton publicly as they have jetted across Southeast Asia. They met up in Thailand and then traveled together on Monday to Myanmar and finally here to Cambodia. Along the way, they teamed up to meet with premiers and potentates, tour an ancient golden pagoda and chat with a Buddhist monk about budget deficits and maybe even presidential politics.

On the porch of the house of Myanmar’s opposition leader, Daw Aung San Suu Kyi, Mr. Obama gave Mrs. Clinton a shout-out.

“Where did Hillary go?” he suddenly asked as he interrupted his remarks about Myanmar’s transition from military rule. “Where is she?”