By Andrew Scurria and Soma Biswas

The law firm representing one of Elliott Management Corp.'s biggest private-equity bets has resigned after steering a debt deal that angered some of the legal adviser's prominent Wall Street clients, according to people familiar with the matter.

Kirkland & Ellis LLP, one of the most powerful law firms in finance, resigned from representing Travelport Worldwide Ltd. after the U.K.-based travel-booking company touched off a legal confrontation with corporate-debt investors that Kirkland also counts as clients, these people said.

The dispute arises from a $1 billion financing deal supplied by Elliott and private-equity firm Siris Capital Group to help protect their stakes in Travelport during the coronavirus pandemic after they took the company private last year in a $2 billion deal.

The loan package depends on shifting valuable intellectual property assets out of the grasp of Travelport's lenders, including the debt-investing divisions of Blackstone Group Inc. and Bain Capital LP, which have hired Kirkland on other matters surrounding their private-equity businesses, people familiar with the matter said.

Those investors, represented by law firm Akin Gump Strauss Hauer & Feld LLP and financial adviser PJT Partners Inc., have said the transaction isn't allowed under Travelport's $2.9 billion first-lien loan and have accused the company of defaulting on its debt, according to people familiar with the matter.

A New York court might get the final say on whether the company acted within its rights. Travelport filed a lawsuit Friday seeking declaration that a default hasn't occurred.

The financing deal is backed by intellectual-property assets that were previously within the lenders' reach but are now pledged to Elliott and Siris as collateral. Several private-equity owned companies advised by Kirkland have tried similar maneuvers in recent years, taking advantage of flexible debt agreements to move assets away from creditors and free up collateral for fresh financing.

The Travelport deal has pitted heavyweights in the debt-investing business against each other, with Elliott on one side and Blackstone's GSO Capital Partners LP on the other. The lenders' group, which includes GSO, Bain, Ares Management Corp. and Canyon Partners LLC, has proposed a rival $500 million loan package to help Travelport weather the pandemic, a person familiar with the matter said.

Kirkland was caught in the middle, people familiar with the matter said. The law firm decided it wasn't possible to continue representing Travelport given the extremely contentious dynamics between the shareholders and lenders, one of the people said.

Such a resignation is unusual for any firm, let alone one as dominant as Kirkland, which has been outpacing its peers during the coronavirus pandemic in advising troubled companies on seeking relief from creditors.

U.K.-based Travelport competes with rivals Amadeus IT Group SA and Sabre Corp. in the business of linking airlines with booking websites and travel agents. Falling air-transit volumes during the pandemic have dented revenue at Travelport, which also missed out on cash it expected from a $1.7 billion sale of its eNett payments unit when the buyer, WEX Inc., said last month that it was abandoning the deal.

To bridge the shortfall, Travelport started negotiations with lenders for potential financing while also transferring intellectual-property assets into a special subsidiary that would back a new debt issuance.

Travelport sought help from Kirkland, the legal adviser to J.C. Penney Co., Neiman Marcus Group Inc., Whiting Petroleum Corp. and others during their bankruptcies. Law firms that navigate debt restructurings commonly negotiate against investors that are also clients on unrelated matters, according to people familiar with industry practices.

But Travelport has set off an unusually intense standoff after becoming the latest borrower to use a controversial strategy popularized by J.Crew Group Inc. in 2016, when the retailer transferred brands and trademarks to a special subsidiary to secure fresh financing. While that benefited some creditors, others were disadvantaged and sued to reclaim their rights to the branding.

In 2018, Neiman Marcus moved its prized MyTheresa division to a holding company controlled by shareholders and outside the reach of creditors, provoking litigation. J.Crew and Neiman Marcus filed for bankruptcy last month, before final court rulings on whether the asset moves were allowed.

The groundwork for these disputes was laid as lenders, eager to squeeze out meager returns from the corporate debt market, accepted fewer and fewer protections in recent years when investing.

Write to Andrew Scurria at Andrew.Scurria@wsj.com and Soma Biswas at soma.biswas@wsj.com