Live From Twitter, It’s Elon Musk Show. Next Up, New CEO and Tucker Carlson

“It’s entertaining," Mr. Musk said at a marketers’ conference last month, one of many stops on a publicity tour that was supposed to calm Twitter advertisers. Then, he added: “Train wrecks are arguably entertaining."

Forget HBO’s “Succession." For the past year, one of the hottest dramas in the media world has been playing out at Twitter—and on Twitter—with the billionaire entrepreneur as the main character.

And it is all unfolding before uneasy advertisers, many of whom bailed from the platform after Mr. Musk took control more than six months ago.

This week previewed an upcoming season that looks equally as spicy. New characters were teased and story lines emerged, including: the arrivals of Tucker Carlson as the canceled newsman looking for a new stage to perform on and a new leading lady to run Twitter as chief executive.

Mr. Musk plans to take a new role as executive chairman and chief technology officer of the social-media company.

On Thursday afternoon, Mr. Musk scripted a cliffhanger by not actually naming his CEO, instead tweeting only that he had hired a woman to take the role in about six weeks. The statement set off wild speculation on Twitter over whom it might be, from pop star Taylor Swift to “Succession’s" own fictional Shiv Roy.

By that evening, The Wall Street Journal reported Ms. Yaccarino was in talks for the job. Around lunchtime Friday in New York, Mr. Musk confirmed in a tweet that Ms. Yaccarino was, in fact, the one.

Her appointment now sets the stage for more drama. How she navigates an owner with a history of saying he doesn’t want to be CEO but who doesn’t fully relinquish control will be a central plotline in the coming months. Mr. Musk has frequently described himself as a “nano-manager" at the other companies he runs, such as automaker Tesla and rocket company SpaceX.

The Twitter drama began last spring when he surprisingly revealed he had taken an ownership stake in the then-publicly traded social-media company, followed by up-and-down battles for control of the firm that culminated in his taking it private in a $44 billion deal.

The succession drama began soon after his late October takeover with a pledge to hire for the CEO role.

His ambitions for Twitter are to build new technical capabilities, such as secure messaging and banking features that will help the company become a much bigger business. Meanwhile, he is stuck with a firm mostly dependent on advertising sales.

Between tweets and news headlines, it all can look like chaos—cost cuts, employee exoduses and tweet storms. Even President Biden mocked Mr. Musk after the billionaire tweeted that National Public Radio should be defunded.

“The best way to make NPR go away is for Elon Musk to buy it," the president said two weekends ago at the annual White House Correspondents’ Association dinner.

All of that chaos may be some of the point, according to George Hotz, an engineer who worked at the social-media company during the new owner’s early days.

“The source of Elon’s power. It comes from a new theory of management," Mr. Hotz wrote in a personal blog after he left Twitter in December. “By continually creating chaos, process is incapable of forming, and everyone is forced to work only toward goal."

With Twitter, ultimately, Mr. Musk has said he wants to safeguard it as a haven of free speech, even if controversial.

His efforts have attracted Mr. Carlson, who on Tuesday said he would bring his TV show to the social-media platform after getting ousted last month by Fox News, whose parent company shares common ownership with the Journal.

The cable channel’s most-watched prime-time host has cultivated a large fan base of right-leaning viewers. His arrival could help increase traffic, which is important because Mr. Musk needs to keep Twitter relevant in pursuing his broader reinvention.

But it isn’t finalized. Questions remain if as to whether Mr. Carlson’s contract with Fox News will allow him to create a new show on Twitter and what it would look like. Mr. Musk also risks further unnerving advertisers who’ve already been spooked by the billionaire’s own outspoken nature on Twitter.

That’s the scene into which his new CEO will enter.

Even Mr. Musk has admitted it is hard to find a candidate for his world. A week before the marketers conference with Ms. Yaccarino, Mr. Musk told a reporter he didn’t have anyone in mind. Instead, he called his dog the actual CEO.

But his appearance at that influential marketers conference on April 18 in Miami Beach, Fla., showed Mr. Musk could be made more palatable to advertisers, if helped by a deferential but shrewd approach.

On stage as the moderator, Ms. Yaccarino was just that.

She prodded Mr. Musk to reassure marketers in the room, who, she said, were his “accelerated path to profitability" but are also skeptical of him and “need to feel that there is an opportunity for them to influence what you’re building."

“They’re challenged by separating the man, his opinions and the microphone that he now owns," Ms. Yaccarino told him. She then pushed him to commit to reining himself in on Twitter, noting that even he has said he probably shouldn’t tweet after 3 a.m.

Mr. Musk said he’d try to curb his tweets after 3 a.m. but also drew a hard line. “If I were to say, ‘Yes, you can influence me,’ that would be wrong," he said. “It would be very wrong. It would be a diminishment of freedom of speech."

She clarified on the idea of “influencing," suggesting he needed “an open feedback loop" with advertisers to excite them to spend more money.

He appeared to hear her, saying he would be open to listening to their feedback. “But it is not cool to try to say what Twitter will do. And if that means losing advertising dollars, we lose it."

It sounded like a detente. Or, at least, a mutual understanding. And as she concluded the almost 40-minute discussion, Ms. Yaccarino turned her attention to the audience, urging them to work with Mr. Musk. “You’ve got a man," she said, “who’s committed to try his best not to tweet after 3 a.m. [and] open to your feedback."

On Thursday, in another plot twist, he dropped his tweet about hiring a Twitter CEO. Ms. Yaccarino was busy with dress rehearsals for her NBCUniversal job, preparing for a crucial presentation to advertisers to sell the coming TV season.

As night fell, Mr. Musk kept coy on if it was truly her. Shortly before 3 a.m. Friday in New York, he tweeted: “The most entertaining outcome is the most likely."

Write to Tim Higgins at tim.higgins@wsj.com