For more than a decade, the Clinton Global Initiative was the star-studded marquee attraction during the annual meeting of the United Nations General Assembly, a place where heads of state, celebrities, billionaire philanthropists and business people mingled, made deals and gave away millions, sometimes billions, of dollars.

But after Bill and Hillary Clinton announced the end of their signature conference during last year’s presidential campaign, Michael R. Bloomberg, the former mayor of New York and billionaire, has stepped unto the breach.

On Wednesday, Mr. Bloomberg will host a reorganized and rebranded Bloomberg Global Business Forum at the Plaza Hotel, drawing a high-powered crowd and speakers from Tim Cook, the chief executive of Apple, to President Emmanuel Macron of France.

In a symbolic passing of the guard, Mr. Clinton will be the first speaker on the day’s agenda almost exactly a year after he urged attendees “you have to keep this alive” in a farewell address at the last Clinton Global Initiative.