A judge may take up whether her father should be ousted as her conservator, and whether the arrangement should be ended entirely.[Follow live updates on Britney Spears’s conservatorship hearing.]Some changes have come quickly in the three months since Britney Spears spoke up publicly for the first time about the conservatorship that has overseen her life for more than 13 years, calling the arrangement abusive and exploitative at a hearing on June 23.For the first time in the case, Ms. Spears, 39, was allowed to hire her own lawyer, replacing a court-appointed one. A bank that was set to begin managing the singer’s money, alongside her father, resigned, as did her longtime manager. And Ms. Spears, who said she believed the conservatorship would prevent her from getting married or having a baby, got engaged to her boyfriend, Sam Asghari.But other changes Ms. Spears has been seeking to the conservatorship — in some cases for many years — remain open questions as the case returns to a Los Angeles courtroom for its latest status hearing.Ms. Spears’s new lawyer, Mathew S. Rosengart, doubled down in recent weeks on his attempts to remove the singer’s father, James P. Spears, as the conservator of her estate, calling him actively harmful to her well-being and asking for further investigation into Mr. Spears’s conduct. Mr. Rosengart has said in court documents that he will move to terminate the conservatorship entirely this fall.Yet even as Mr. Spears, 69, reversed course this summer, agreeing to step aside eventually before filing to end the conservatorship altogether earlier this month, he has continued to push back against his immediate suspension or removal.These are some of the questions that could be decided by the probate judge in the case, Brenda Penny, on Wednesday. The hearing is set to begin at 4:30 p.m. ET.Will the Conservatorship Be Terminated Altogether?At this point, Ms. Spears has not officially filed to end the conservatorship. In a twist this month, lawyers for Mr. Spears, who had long maintained that the conservatorship was voluntary and necessary, did file to end it, citing the singer’s stated wishes and recent shows of independence. But experts have said that terminating a conservatorship without a medical evaluation — as Ms. Spears and now her father have asked for — is unlikely, and there is no public record of the judge calling for a psychiatric evaluation recently. (In 2016, according to confidential documents obtained by The New York Times, a court investigator said the conservatorship remained in Ms. Spears’s best interest despite her requests to end it, but called for a path to independence.)Mr. Rosengart has called Mr. Spears’s attempt to terminate the arrangement “vindication” for Ms. Spears, but suggested that the singer’s father was attempting to “avoid accountability and justice, including sitting for a sworn deposition and answering other discovery under oath” by filing to end it.In a filing last week, Mr. Rosengart said that Ms. Spears “fully consents” to terminating the conservatorship and said that Ms. Spears’s personal conservator since 2019, Jodi Montgomery, backed it as well, “subject to proper transition and asset protection.” But he called for “a temporary, short-term conservator to replace Mr. Spears’s until the conservatorship is completely and inevitably terminated this fall.”Will Jamie Spears Be Removed as Conservator?“While the entire conservatorship is promptly wound down and formally terminated, it is clear that Mr. Spears cannot be permitted to hold a position of control over his daughter for another day,” Mr. Rosengart wrote in his filing last week. “Every day Mr. Spears clings to his post is another day of anguish and harm to his daughter.”Ms. Spears’s lawyer has moved to replace her father on a temporary basis with John Zabel, a certified public accountant in California who has worked in Hollywood.Yet Mr. Spears maintained in filings this week that while there is “no adequate basis” for his suspension or removal as conservator of the estate, the court should instead focus on terminating the conservatorship — something that is “opposed by no one” and should take priority. (Lawyers for Mr. Spears contend that in 13 years, “not a single medical professional nor the report of a single probate investigator has recommended that Mr. Spears’ presence as Conservator was harming Ms. Spears.”) Ending the conservatorship, Mr. Spears’s lawyers wrote, “would render some of the other pending matters moot” and “would provide an incentive for the resolution of all other matters.”At the same time, Mr. Spears’s lawyers also argued that Mr. Zabel “does not appear to have the background and experience required to take over a complex, $60 million” estate immediately, pointing to Mr. Zabel’s personal losses in a real estate investment. Mr. Rosengart countered on Tuesday that Mr. Spears has “zero financial background,” a previous bankruptcy and faces allegations of abuse.Will Mr. Spears and Others Be Investigated Further?Following Ms. Spears’s comments in June — in which she said she had been forced to take medication and was unable to remove a birth-control device — her father asked the court to investigate the claims, denying his own culpability and instead calling into question the actions of Ms. Montgomery, the singer’s current personal conservator, and others.Mr. Rosengart has since asked for a future hearing on outstanding financial issues involving the conservatorship, calling mismanagement of Ms. Spears’s estate by her father “evident and ongoing.” He said that Mr. Spears had been served a request for discovery and a sworn deposition in August, before he filed to end the conservatorship.So far, the judge has not addressed potential investigations, and additional financial matters — including disputed fees for various lawyers in the case and accounting for the conservatorship covering 2019 — remain outstanding. In their filing this week, lawyers for Mr. Spears said that “all pending issues could be resolved” if the judge called for a mandatory settlement conference of private mediation.“The last thing this Court or this Conservatee needs or wants would be extended and expensive litigation over pending or final accounts and fee petitions,” they wrote.Will Recent Revelations Be Addressed?Since the last hearing in July, three documentaries about the Spears conservatorship have been released, in addition to related reporting on the case. “Controlling Britney Spears,” the second documentary on the subject by The New York Times, revealed that an intense surveillance apparatus monitored the singer, including secretly capturing audio recordings from her bedroom and accessing material from her phone.Recording conversations in a private place and mirroring text messages without the consent of both parties can be a violation of the law. It is unclear if the court overseeing Ms. Spears’s conservatorship approved the surveillance or knew of its existence. Ms. Spears’s lawyer called for an investigation, writing in a court filing on Tuesday that Mr. Spears “crossed unfathomable lines,” further supporting the need to suspend him immediately.A Netflix film, “Britney Vs. Spears,” reported that Ms. Spears sought to end the conservatorship beginning in 2008 and 2009, raising concerns about her father’s fitness for the role, the money she was making for others and threats involving custody of her children. Documents obtained by the filmmakers also showed that Ms. Spears’s access to medication she liked increased when she worked, including during a stint as a judge on “The X-Factor” in 2012. More