LOS ANGELES — Robert A. Iger has extended his reign at the Magic Kingdom for a third time, as an heir continues to be difficult to find.

The Walt Disney Company said on Thursday that Mr. Iger, 66, will remain chief executive and chairman until July 2019, an extension of one year beyond his previously pushed back retirement date, reflecting a continuing streak of success at the world’s largest entertainment company but also the lack of a clear successor.

“It is obvious that the company and its shareholders will be best served by his continued leadership as the board conducts the robust process of identifying a successor and ensuring a smooth transition,” Orin C. Smith, Disney’s lead independent director, said in a statement. Mr. Smith noted Mr. Iger’s “record of success in a changing media landscape, and his clear strategic vision for Disney’s future.”

Under the contract extension, Mr. Iger’s compensation will be determined on the same basis as before, according to a securities filing. But the new deal provides for a $5 million bonus if he completes the term. He will also remain close to the company after stepping down: The extension calls for him to serve as a consultant for three additional years, with pay of $2 million for each of the first two and $1 million for the third.

An extension has been widely expected. After insisting last year that he would stick to his retirement plans, Mr. Iger recently softened his position. “While I am confident that my successor is going to be chosen on a timely basis and chosen well, if it is in the best interest of the company for me to extend my term, I am open to that,” he told analysts during a February conference call.

Disney’s share price climbed on Thursday morning after the news.

The question now is who will follow him. Since he took over in 2005, Mr. Iger has led Disney to record financial results, even in the face of economic downturns, the occasional horrendous movie write-off and changing consumer habits that have dented ESPN, its primary profit engine.

The downside: Nobody can seemingly measure up, complicating succession at a company that has a terrible track record on that front. The obvious internal candidate to succeed Mr. Iger, the well-regarded Thomas O. Staggs, abruptly left Disney last year after losing the unqualified support of Mr. Iger and some other board members. Since then, Disney has been engaged in a quiet hunt for a successor, including looking outside the company.

Mr. Iger, who is also a member of the Apple board, started his entertainment career at ABC in 1974. Disney has no mandatory retirement age for chief executives; the company’s mandatory retirement age for board members is 74.