Those advisers have long championed supply-side economics and reject the hard-line position on trade that one side’s gain must come at the other’s expense. By offering more carrots—slashing red tape and taxes to make the U.S. the top destination for businesses—they say stronger growth would obviate any need for trade protectionism.

“It is the supply-siders versus the zero-sum crowd,” said Andy Laperriere, political strategist at research firm Cornerstone Macro LP who closely watches such policy developments.

A third group of advisers are mostly business associates of Mr. Trump’s who aren’t particularly ideological.

The question is in which direction Mr. Trump will go. The coming weeks of White House staffing and policy briefs have taken on even greater importance to markets and industry because Mr. Trump hasn’t held elective office, honed a consistent political ideology or cultivated a bench of trusted advisers. His campaign didn’t issue the types of detailed policy papers typical of past presidential runs.

Mr. Trump has blamed bad trade deals for the loss of U.S. jobs and promised to renegotiate and potentially quit the 1994 North American Free Trade Agreement with Canada and Mexico, calling it the worst trade deal “maybe ever signed anywhere.” He called the 12-nation Trans-Pacific Partnership, completed last year but not yet approved by the U.S., a “continuing rape of our country.”

As Indiana governor, Mr. Pence had supported the TPP but reversed his support for the pact and earlier free-trade agreements after Mr. Trump tapped him to join the ticket.

David Malpass, the economist handling the economic portfolio for the transition effort, declined to comment. Other advisers have dismissed talk of strains. “What we’re seeing is a very orderly group of people working on behalf of the American people,” said Anthony Scaramucci, a member of the transition team executive committee who manages hedge-fund firm SkyBridge Capital, to reporters in New York on Thursday.

Key appointments extend not only to cabinet-level positions at the Treasury and Commerce departments but also to possibly more influential roles such as director of the National Economic Council and chairman of the Council of Economic Advisers.

Those picks could shape the extent to which Mr. Trump governs as a more traditional Republican focused on cutting taxes and regulation or as an antiestablishment populist who pushes ahead with more tariffs and taxes on companies that outsource jobs.

So far, broad agreement between the two camps of advisers over the necessity of reducing taxes and regulations have allowed them—and the broader GOP—to paper over the bigger disagreements on trade. “There will be a balancing act,” said Stephen Moore, a top economic adviser during the campaign on taxes who disagrees with Mr. Trump on trade. “There’s going to be some disagreements even within the administration about what should be the priority…I don’t know how that will all come down.”

Advisers in both camps say Sen. Jeff Sessions (R., Ala.)—a longtime proponent of tighter trade and immigration rules—has emerged as the most influential adviser to Mr. Trump on the economy. Mr. Trump said Friday he would nominate Mr. Sessions as attorney general. The Republican senator’s former senior aide, Stephen Miller, became Mr. Trump’s national policy director.

In the final weeks of the campaign, Mr. Trump’s speeches reflected the view of advisers who share a deep skepticism of trade deals, including economist Peter Navarro, financier Wilbur Ross and steel executive Dan DiMicco, all of whom are being considered for top posts in the new administration.

Mr. Navarro, a professor at the University of California, Irvine, has written several books sharply critical of China’s trade and labor practices, including his 2008 publication, “The Coming China Wars,” and his 2015 book, “Crouching Tiger; What China’s Militarism Means for the World.”.

Mr. Navarro learned from a television interview that Mr. Trump was a fan of his writing, and the two struck up a correspondence several years ago. Mr. Navarro became an adviser to the campaign earlier this year, though he and Mr. Trump hadn’t met in person until September.

Mr. Laperriere said markets aren’t taking seriously enough Mr. Trump’s tough talk on trade, in which he equates trade deficits with theft. While the White House needs Congress to approve tax cuts, Mr. Trump has wide authority to change trade policy unilaterally.

On a range of other policy issues, Mr. Trump sounds as if his position “could easily evolve,” Mr. Laperriere said. “By contrast, his convictions on trade appear strong.”

Lawrence Kudlow, the CNBC commentator who advised Mr. Trump earlier this year on taxes, criticized using the trade deficit as a scorecard for whether the U.S. is winning or losing from trade. “Peter Navarro, a friend, is just wrong,” he wrote on Twitter before the election. Trade deficits, he added, simply reflect capital inflows and not forgone economic gains.

Mr. Kudlow also implored the campaign to tamp down the tariff talk. By following through with tax relief for large and small businesses, “these companies won’t leave in the first place,” Mr. Kudlow told Mr. Pence in a radio interview before the election.

“My response,” replied Mr. Pence, “is you’re exactly right.”