Queen Elizabeth II’s death could hasten efforts by some countries to reassess their relationship with the British Crown, and provide momentum to activists who have long argued that their nations shouldn’t have a foreign ruler as head of state.

The British monarch, now King Charles III, is the official head of state in 14 countries outside of the United Kingdom. They include Australia, New Zealand and Canada, as well as several Caribbean and Pacific island nations.

Queen Elizabeth was a beloved figure who in her 70 years on the throne provided a sense of stability and constancy to millions of people worldwide, and she established a personal connection with many ordinary citizens in her dozens of state visits overseas. But with the accession of the less-popular King Charles, republican campaigners have an opportunity to argue their position without being seen as insulting a well-liked queen.

“I do think there will be change,” said Areti Metuamate, an indigenous Māori from New Zealand who has been active in republican movements and works in academia. “I think people will start to really think more about it now.”

Even before the queen’s death, some countries had signaled that their time with the monarchy, a relationship that originated with colonialism, should end. Last year, Barbados became the first country in about 30 years to ditch the monarchy. Several other Caribbean nations, including Jamaica, are preparing to sever ties.

In an interview published Sunday, the prime minister of Antigua and Barbuda, Gaston Browne, told British television network ITV News that he wants to hold a referendum on his country becoming a republic, possibly within three years. Antigua and Barbuda is a former British possession in the Caribbean.

A poll published in April from the Angus Reid Institute indicated nearly 60% of Canadians supported moves by countries such as Barbados and Jamaica to cut ties with the British monarchy. And half of Canadians said they didn’t think their country should continue as a constitutional monarchy for coming generations.

“Condolences, of course, and credit to her unwavering commitment to duty,” Citizens for a Canadian Republic, a group that supports abolishing the monarchy, tweeted after the queen died. “But as Canadian republicans, we must all be ready to present our case for a 21st-century non-monarchical alternative to succession.”

Tom Freda, a spokesman for the Canadian group, declined to comment further about whether it would be easier now to make the case for a republic. “We don’t want to exploit the queen’s death,” he said.

Australian Prime Minister Anthony Albanese lays a wreath next to Queen Elizabeth II’s statue at Parliament House in Canberra, Australia.

Photo: mick tsikas/Shutterstock

The debate has intensified in Australia, where voters in 1999 rejected a constitutional amendment to abolish the monarchy. Recent polls have shown more Australians support establishing a republic than keeping the monarchy, though many are undecided. Australia’s center-left prime minister, Anthony Albanese, refocused public attention on the issue when he appointed an assistant minister for the republic after winning an election in May.

In a television interview Sunday with Sky News U.K., Mr. Albanese said that now is the time to pay tribute to the queen and that he wouldn’t commit to holding a referendum on becoming a republic in his first term, which could run into 2025.

Until the 1980s, many Australian court decisions could still be appealed to the U.K. The governor-general, the monarch’s representative, still has certain powers, such as issuing a writ, or legal ruling, ordering a general election. The power is exercised on the advice of Australian ministers, but in some circumstances the governor-general is considered to have the power to act independently. Controversially, the governor-general dismissed Prime Minister Gough Whitlam in the 1970s.

The monarchy’s days in Australia appear to be numbered, said Cindy McCreery, an expert in monarchy and colonialism at the University of Sydney. Queen Elizabeth’s 1954 visit to Australia, the first by a sitting British monarch, drew massive crowds at a time when many Australians had a personal connection to the U.K. But fewer Australians today have that affinity, as many were either born in Australia or have migrated from other countries, she said.

One issue in Australia would be how to choose its head of state if it isn’t the British monarch. The 1999 referendum suggested that parliament appoint a president by a two-thirds majority, which some Australians believed gave too much power to politicians. One new proposal from the Australian Republic Movement suggested that each Australian state and territory, and the federal parliament, nominate candidates who would then be put to a popular vote.

Dr. McCreery said she didn’t expect any immediate push from the government to abolish the monarchy, out of respect for the queen.

After her death, Mr. Albanese spoke warmly of the queen, noting her 1954 visit was important to his mother, who he remembered telling him about the event. Many Australians flocked to churches to pay their respects and left flowers outside government buildings. The sails of the Sydney Opera House were lighted up in the queen’s honor.

“For all of us, wherever we are on this planet, and that would include America, this is the only monarch that most of us have ever known,” Dr. McCreery said. “This is a huge change for many of us, even if we don’t necessarily consciously realize it today.”

Some supporters of the monarchy said they weren’t concerned for the future. Jarrod Bleijie, a lawmaker in the legislature of Australia’s Queensland state and a spokesman for the Australian Monarchist League, said Australians would ultimately favor the stability provided by the current system.

“If we look at democracies around the world, the most stable democracies are constitutional monarchies,” he said. “Australia will support our new king.”

New Zealand's Prime Minister Jacinda Ardern speaks at a Proclamation of Accession ceremony for King Charles III in Wellington, New Zealand.

Photo: andrew turner/Agence France-Presse/Getty Images

In neighboring New Zealand, Prime Minister Jacinda Ardern has previously said her country could transition away from the monarchy in her lifetime. On Friday, she described the queen as a widely admired and extraordinary monarch.

Tackling the monarchy question hasn’t been a priority for Ms. Ardern’s government, said Katie Pickles, a history professor at the University of Canterbury. One complication, she said, is that a treaty viewed as a founding document of New Zealand is between the indigenous Māori and the British Crown.

“We’ve been the most reticent to change of just about anywhere in the Commonwealth,” she said, pointing out that New Zealanders in 2016 voted against removing the Union Jack from the national flag.

Still, some lawmakers have campaigned for a republic. Earlier this year, the small Māori Party called for removing the British monarch as head of state.

Mr. Metuamate said he respected the queen and the gracious way she acted throughout her reign. But explaining to his 2-year-old son, who has both Māori and indigenous Australian heritage, why he couldn’t be the head of state of either country under the current system would be a struggle, he said.

“Imagine that in America,” he said. “That would never be acceptable, that the equivalent of the president could live in England.”

Even if public opinion in countries like Canada is that they no longer want the monarchy, installing a republic faces significant legal hurdles, constitutional experts say. Canada’s constitution requires the unanimous consent from the country’s federal parliament and all 10 provincial legislatures. That is a high threshold to reach, Canadian legal experts say, citing failures in recent decades to reach consensus on constitutional changes.

Write to Mike Cherney at mike.cherney@wsj.com and Paul Vieira at paul.vieira@wsj.com