For years, through carefully choreographed dinners and meetings, Apple CEO Tim Cook did something that has eluded many other corporate leaders: He developed a personal relationship with President-elect Donald Trump.

Their rapport has been built, in part, by zeroing in on areas of mutual interest between Apple and Trump’s agenda.

Now, with Trump’s cabinet taking shape and new circles of power emerging in Washington, executives across the corporate sphere are working to get in the good graces of the new administration. Plenty hope to follow Cook’s playbook.

In the first Trump administration, the Apple executive pioneered a template for how business leaders should engage with Trump. Instead of sending government relations executives or lobbyists, Cook would appeal to Trump directly through phone calls and meals, said people familiar with the interactions.

Cook then developed a meeting strategy with Trump where he would bring one data point to home in on a single issue in a meeting, the people said. That approach helped keep the meetings from spiraling in too many directions.

Big win on tariffs

In 2017, as Trump was working on a tax-cut plan, Cook told the then-president that Apple would increase its U.S. investments if the company could repatriate $250 billion in overseas cash at a reduced tax rate. Trump would later cite Apple while promoting his tax plan.

Cook’s biggest win took place in 2019 when Apple was facing down a potential 10% tariff on all imports from China, where Apple still overwhelmingly produces its devices. Cook personally lobbied Trump, explaining how tariffs would increase iPhone prices and help foreign rivals like Samsung . Days later, the Trump administration announced it would scale back its tariff plan, giving exceptions to a range of electronics, including the iPhone.

Apple then reversed an earlier decision to move production of its Mac Pro computer to China from Austin, Texas. Trump appeared with Cook in Austin at the site of the manufacturer and later tweeted that he had “opened” a major Apple manufacturing plant. The plant, operated by a contractor, had actually been open for years. Neither Cook nor Apple corrected Trump’s claim.

Trump personally reveled in the attention Cook gave him and praised him for directly engaging. “That’s why he’s a great executive, because he calls me and others don’t,” Trump said of Cook in 2019.

Even before Trump was again elected president, Cook resumed his engagement with Trump. On a podcast in October, Trump said Cook called him about Apple’s growing legal problems in Europe. Apple is facing massive fines for violating EU competition laws. Trump said he told Cook: “I’m not going to let them take advantage of our companies.”

Apple didn’t respond to requests for comment.

Benefits and risks

Replicating Cook’s playbook will likely prove challenging, executives say. Few companies carry the name recognition of Apple and Cook. Some lobbyists and corporate advisers have already found that, if Trump doesn’t have an existing relationship with an executive, getting on his schedule now is difficult.

If a company is well known, that helps; Boeing CEO Kelly Ortberg spoke with Trump in recent days and discussed trade policies and tariffs. Ortberg initiated the call, which was mainly to congratulate Trump on his victory, according to people familiar with the discussion. The two don’t have a prior relationship and Trump had been critical of the jet maker in his first term.

Like many executives, Cook also leveraged middlemen. During Trump’s first term, Cook cultivated close ties with his son-in-law Jared Kushner and daughter Ivanka Trump to get to the president.

Those who sit down with the president-elect or others in his circle of power should know that there are both benefits and potential risks to doing so, said Ron Williams , a former CEO of health insurer Aetna, and a board member at companies such as Warby Parker.

“Anytime you can build a relationship with someone, you are advantaged,” Williams said. “If you have dinner, you can count on your phone ringing at some point; that may or may not be what you want.”

Williams has found it can be helpful to be a source of information and data to government officials. When he was running Aetna, Williams said he tried to provide fact-based context on health policy to government officials, explaining implications of proposed changes, to simplify complicated matters.

Developing such relationships takes time and a strategy. For example: Is it best to shoot for a cabinet-level meeting, or to chat with a committee in the House of Representatives?

“Unless you’re Tim Cook, you have to meet these people three or four times before they know who you are,” Williams said. “You have to invest the time in building the relationships, and the question is where do you do that?”

‘DOGE’ team ideas

Some executives are relying more heavily on trade groups or working to retain in-the-know lobbyists and advisers who have ties with those in Trump’s orbit. A number of companies are also considering whether to propose ideas directly to the “Department of Government Efficiency,” led by Elon Musk and biotech entrepreneur Vivek Ramaswamy .

If executives can offer ideas to streamline the government, aligning on issues the administration cares about, it could be a way to develop new relationships within Trump’s inner circle. How executives do that remains unclear, as the DOGE team and others still are taking shape.

“We will continue to build relationships with the new administration,” said Aradhana Sarin , chief financial officer at AstraZeneca , while noting that she is unsure if the pharmaceutical giant will suggest ideas to the efficiency group.

Others are planning alternative paths to reach the new administration. One technology CEO said that, with so many venture capitalists in Trump’s orbit, he plans to lean more on his venture-capital investors for influence in Washington instead of relying on traditional lobbying firms.

Not all one-on-one engagement achieves the desired results. FedEx chairman Fred Smith , an advocate of free trade, said at an event last month that he has spoken to Trump “very vociferously” about globalization and tariffs.

“I haven’t been able to move him. He says imports are deficits or losses and exports are profits,” Smith said of Trump at the time. “But I’ve pointed out to him, and he’s very kind, he’s actually a very nice fellow one-on-one.”

A spokesperson for the Trump transition team didn’t respond to a request for comment.

Following Trump’s win in the 2024 presidential race, Cook congratulated him and suggested their relationship would continue.

“We look forward to engaging with you and your administration,” Cook wrote on social media.

Write to Chip Cutter at chip.cutter@wsj.com and Aaron Tilley at aaron.tilley@wsj.com