LONDON—Prince Andrew’s decision to settle allegations of sexual abuse removes the immediate threat of a highly publicized trial, but the aftershocks of the yearslong scandal continue to reverberate in Buckingham Palace.

Virginia Giuffre filed a suit last year alleging disgraced financier Jeffrey Epstein and British socialite Ghislaine Maxwell forced her to have sex with the royal when she was a teenager in the early 2000s. Prince Andrew repeatedly denied the charges, said he had never met Ms. Giuffre and then requested a jury...

LONDON— Prince Andrew’s decision to settle allegations of sexual abuse removes the immediate threat of a highly publicized trial, but the aftershocks of the yearslong scandal continue to reverberate in Buckingham Palace.

Virginia Giuffre filed a suit last year alleging disgraced financier Jeffrey Epstein and British socialite Ghislaine Maxwell forced her to have sex with the royal when she was a teenager in the early 2000s. Prince Andrew repeatedly denied the charges, said he had never met Ms. Giuffre and then requested a jury trial.

On Tuesday, his representatives said he settled the matter for an undisclosed sum. The announcement raised questions about whether Prince Andrew could afford to pay without financial help from his mother, Queen Elizabeth, and what now lies in store for the prince.

“We have never commented on the financial arrangements of the Duke’s private legal matters and will not be doing so now,” said a spokesman for Buckingham Palace, which speaks on behalf of the royal family.

In a statement, the prince didn’t admit wrongdoing. He pledged to “demonstrate his regret for his association with Epstein by supporting the fight against the evils of sex trafficking, and by supporting its victims.” Prince Andrew will make a substantial donation to Ms. Giuffre’s charity.

Ms. Giuffre’s lawyer said on Monday that the settlement speaks for itself.

“I can’t see any way of him coming back into public life,” said Nick Goldstone, head of dispute resolution at law firm Ince Gordon Dadds LLP in London. “The U.K. public hate the prospect of public money or the queen’s money going to protect someone who was demanding a trial jury and now has run away.”

It is unclear what the future holds for the 61-year-old prince. He currently resides in the Royal Lodge, a 30-room house on the Windsor estate he shares with his ex-wife Sarah, Duchess of York. Experts on royal finances say that Prince Andrew likely receives financial support from the queen. He also has a pension from when he served in the Royal Navy and owns a chalet in Switzerland. It couldn’t be determined if his security costs are covered by U.K. taxpayers.

On Tuesday, a meme was trending showing a photo of a long line of people and a joke: “Huge queue forms at Palace on news that Prince Andrew is giving away money to people he’s never met.”

Others urged that the prince, who has already been stripped of his military affiliations and royal patronages, also be relieved of the title Duke of York. Rachael Maskell, a lawmaker representing the city of York in northern England, said the affiliation with the prince had caused her district hurt and embarrassment. Such a move would require an act of parliament.

Prince Andrew settled a sex-abuse lawsuit filed by Virginia Giuffre.

Photo: Bebeto Matthews/Associated Press

Buckingham Palace has gone to great lengths to put space between the prince and the monarchy. His ties with Epstein proved an unwanted sideshow as the monarchy lays the groundwork for a delicate succession from Queen Elizabeth to her eldest son, Prince Charles.

In part at Prince Charles’s request, Prince Andrew has spent just over two years in effective royal exile after stepping back from duties following a failed attempt to clear his name with a 2019 tell-all interview. He is rarely seen in public and has been barred from nearly all ceremonial events, with the exception of his father’s funeral last year. Last month, the palace said Prince Andrew would defend his case as a private citizen.

Palace officials had been bracing for a trial in the autumn, for which Prince Andrew would have had to answer questions under oath. The settlement avoids that prospect as the monarchy celebrates Queen Elizabeth’s 70 years on the throne with a series of street parties and other elaborate pageantry this summer.

Prince Andrew remains a counsellor of state which makes him one of four senior royals who could undertake the Queen’s duties on a temporary basis if she became ill. It is unclear whether the prince will be visible at any of the events that are planned in June to celebrate Britain’s longest-serving monarch.

Buckingham Palace has gone to great lengths to put space between Prince Andrew and the monarchy.

Photo: andy rain/Shutterstock

Even if his name had been cleared at trial, royal commentators question whether his image would have been rehabilitated. Photos that show the prince with his arm around a teenage Ms. Giuffre and taking a walk with Epstein are regularly reproduced in the British press.

Prince Andrew isn’t the only headache facing the crown. Prince Harry, the Queen’s grandson who quit royal duties to live in America, has a book coming out this year. He has previously been critical of officials in Buckingham Palace.

On Wednesday, the British police said that it would investigate allegations that Prince Charles’s charity, The Prince’s Foundation, offered to help secure honors and citizenship for a Saudi businessman who made donations to the foundation. The police said no arrests were made. In a statement, the palace said Prince Charles had no knowledge of the alleged offer.

Before the settlement of a federal sexual assault lawsuit, Prince Andrew was preparing his defense as a private citizen after Buckingham Palace stripped him of royal titles. WSJ looked at how the financial situation of the queen’s second son could have affected the legal battle. Photo: John Thys/AFP/Getty Images The Wall Street Journal Interactive Edition

Write to Max Colchester at max.colchester@wsj.com