At least one longtime sexual abuse victim of Jeffrey Epstein who received a monetary settlement from his estate can also pursue separate claims against two powerful former Wall Street executives who had ties to the convicted sex offender, according to two people briefed on the matter.

Richard Kahn, an executor of Mr. Epstein’s estate, testified in a deposition in May that the victim’s settlement included a “carve out” provision involving Leon Black, a billionaire private equity investor, and James E. Staley, a former top executive at JPMorgan Chase and Barclays, said the people, who were briefed on the deposition and spoke on the condition of anonymity because they were not authorized to publicly discuss the matter.

The exceptions made for Mr. Black and Mr. Staley show how the two men continue to be dogged by their social and business dealings with Mr. Epstein four years after he killed himself in a federal jail while awaiting trial on sex trafficking charges. The arrangement could set a precedent for other victims of Mr. Epstein, potentially exposing Mr. Black and Mr. Staley to further scrutiny and liability.

“She was a victim, potentially, to these individuals,” Mr. Kahn said in the deposition, according to one of the people. Mr. Kahn said that Mr. Epstein’s estate agreed to the carve-out provision so that the unnamed woman could potentially sue for “harms that she incurred.”

In the deposition, Mr. Kahn, who was Mr. Epstein’s longtime accountant, said at least one other victim had sought a similar carve out from the estate, according to the person. He suggested in the testimony, without providing details, that other victims might have asked for the provision with regard to other men, the person said.

It was unclear from Mr. Kahn’s deposition whether either of the women had pursued claims against Mr. Black or Mr. Staley, or what their specific claims might be, the people briefed on the deposition said.

In settling claims with victims, Mr. Epstein’s estate had sought to limit the potential for litigation against anyone with ties to Mr. Epstein. A settlement carve out provides a victim with a limited exception from such a broad release to pursue other litigation.

Both Mr. Black, a co-founder of the private equity firm Apollo Global Management, and Mr. Staley had been frequent visitors to Mr. Epstein’s Manhattan residence. Mr. Black paid Mr. Epstein $158 million for tax and estate planning services — outsize payments that are now drawing scrutiny from the Senate Finance Committee.

Susan Estrich, a lawyer for Mr. Black, said the leak of Mr. Kahn’s deposition testimony “is baseless character assassination” involving “anonymous women who have never brought a claim against Mr. Black.”

Lawyers for Mr. Staley did not respond to a request for comment. A lawyer for Mr. Kahn declined to comment.

The deposition from Mr. Kahn was in connection with a class-action lawsuit filed last year by Mr. Epstein’s victims against JPMorgan Chase, the nation’s largest bank, and a related lawsuit against the bank by the U.S. Virgin Islands.