WEST PALM BEACH, Fla. — As he walked down the red carpet to begin his New Year’s Eve celebrations Sunday night, President Trump stopped to predict “a tremendous year” ahead.

It certainly appeared to be getting off to a lavish start at his Mar-a-Lago club. Before the president arrived — flanked by his 11-year-old son, Barron, and his wife, Melania — a string of guests decked out in jewels, fur and sequins had already streamed in, having paid hundreds of dollars each to celebrate with the president and his family.

But for all the opulence of the annual gala, it was also something else for Mr. Trump: familiar. He has been ringing in the new year at Mar-a-Lago for more than a decade, surrounded by his private club members in the glittering halls of the renovated home of the cereal heiress Marjorie Merriweather Post.