As the Organization of the Petroleum Exporting Countries prepares to meet this week, representatives say there is little mystery about the outcome of the gathering: Any coordinated action on cuts is unlikely.

Instead, the major questions are likely to concern the group’s future after the appointment of its newest representative— Khalid al-Falih, Saudi Arabia’s new energy minister.

Mr. Falih, appointed minister of energy, industry and mineral resources this month, joins a long line of powerful OPEC representatives from the kingdom, by far the group’s biggest producer. They include Sheikh Zaki Yamani, who orchestrated the oil embargoes of the 1970s; and Mr. Falih’s predecessor, Ali al-Naimi, who dominated OPEC decision making for a quarter-century.

But for those two ministers, managing OPEC and thus global oil markets was their main job. Mr. Falih has a full plate of other pressing responsibilities in Saudi Arabia’s increasingly complex energy economy.

Pressure to overhaul that economy, coupled with rising tensions between Saudi Arabia and Iran, also mean that Mr. Falih is operating with much less flexibility when OPEC’s ability to patch up internal differences to make coordinated decisions is already being tested.

“The Falih appointment is clearly about domestic policy more so than international oil policy,” said Yasser Elguindi, an oil analyst at U.S.-based consultancy Medley Global Advisors.

“The coming period is going to be a real test of whether or not OPEC is still alive,” said Mohammad al-Sabban, an independent oil analyst and former senior adviser to the Saudi oil ministry.

Rising prices in recent weeks have taken some of the pressure off OPEC to act at its biannual meeting in Vienna on Thursday. After hitting three-year lows this winter, crude oil prices have nearly doubled and briefly traded above $50 last week, as the global glut that has weighed on the market since 2014 shows signs of unwinding.

There is no specific proposal on production on the meeting’s agenda, said Falah al-Amri, Iraq’s OPEC envoy. That was echoed by several OPEC representatives who met in Vienna ahead of the gathering.

Concerns about Saudi Arabia’s commitment to strengthening OPEC have flared within the group in the run-up to the meeting, as some of the usual outreach to fellow OPEC country representatives has been slow to happen, according to members of the group.

Mr. Falih and other Saudi officials didn’t respond to requests for comment.

Saudi Arabia is at a crossroads, five years after popular uprisings that ousted several regimes in the Middle East, and a little more than a year after the ascension of a new king who will be the last of the sons of Saudi Arabia’s founder to rule.

The king has consolidated power in the hands of his son, 30-year-old Deputy Crown Prince Mohammed bin Salman, over nearly everything that matters in the kingdom, including all the important economic ministries, and has big plans for the country’s energy sector, which is key to even bigger plans for the economy as a whole.

Mr. Falih will play a major role in those plans. He was handpicked by the deputy crown prince, on the heels of the prince’s unusual move last month to spike negotiations between some members of OPEC and key non-OPEC countries over a production freeze.

Prince Mohammed’s 11th-hour intervention, sending the message that there would be no freeze without Iran’s participation, sent shock waves through OPEC by bluntly prioritizing Riyadh’s domestic economic and political goals over those of fellow OPEC members.

That inward focus intensified a few weeks later when Prince Mohammed announced his sweeping plan to overhaul Saudi Arabia’s economy to radically reduce its dependence on oil.

No one is more acutely aware than Mr. Falih of what the transformation plan means for the kingdom’s energy policies and oil-related industries—and how those imperatives limit the kingdom’s dealings with OPEC.

Many other OPEC members are desperately looking for ways to limit production to try to push prices higher.

The foundations of the deputy crown prince’s plans—which includes selling shares of the national oil company, Saudi Arabian Oil Co., known as Aramco, to the public, reducing domestic subsidies for energy and building out the country’s petrochemical industry—are built on Mr. Falih’s work at Aramco, where he was chief executive from 2009 to 2015.

Mr. Falih’s new ministry now includes the country’s power sector. Domestic demand for electricity has skyrocketed in recent years as the population has grown and government subsidies have made power cheap. That directly affects crude exports, as the kingdom burns oil to make about a quarter of its total electricity. As much as 900,000 barrels a day are needed during some hot summer days, almost one in every 10 barrels it produces.

That gives Mr. Falih less flexibility to scale back or ramp up production in response to political developments, to influence prices or even to stabilize the market after unexpected shocks.

“It’s really a new chapter in Saudi oil policy,” said Antoine Halff, an oil economist and fellow at the Center on Global Energy Policy at Columbia University in New York.

Still, many analysts and members of the group believe the Saudis are seeking to avoid confrontation at the meeting, even if they are unwilling to modify their plans to pump as much oil as possible.

Mr. Falih started working at Aramco in 1979 after studying engineering at Texas A&M University. The highlight of his stint at the helm was a historic expansion of the country’s ability to not simply produce crude but also refine it into higher-value products. Aramco built refineries at home and abroad, including in China and the U.S., increasing its capacity to process 5.4 million barrels a day of crude now from around 2.4 million barrels a day in 2009.

Many of those refineries are run as joint ventures in key countries such as the U.S. and China, the two largest buyers of crude in the world and both critical to maintaining Saudi Arabia’s security and geopolitical importance in the world.

The kingdom is negotiating to build a refinery in India, another rising global power analysts say will likely be the fastest-growing energy market over the next few decades.

Mr. Falih also oversaw a significant expansion by Aramco into petrochemicals, using the country’s crude oil as feedstock to make more valuable plastics and industrial chemicals.