The Supreme Court’s eight justices will gather privately on Tuesday to decide what new cases to add to the court’s docket, which could offer some of the first clues about the high court’s direction following the death of Justice Ruth Bader Ginsburg.

They are expected to discuss disputes over the constitutional right to bear arms, cases involving the scope of police immunity from lawsuits, a GOP bid to reinstate Arizona voting restrictions struck down as racially discriminatory, and many other issues.

During their so-called long conference, which marks the unofficial start of the court’s new term, the justices will review hundreds of petitions carried over from last term or filed during the court’s summer recess. They will agree to hear only a handful of these disputes, which will be announced in coming days.

Although Ginsburg’s absence leaves the court with just eight members, the threshold number of justices needed to grant an appeal remains unchanged at four. Yet even before the anticipated confirmation of President Trump’s third Supreme Court nominee, Judge Amy Coney Barrett, creates a 6-3 conservative majority, the internal politics governing the court’s gatekeeping process have likely already changed.

Tuesday’s meeting could not only provide the first glimpse of how the court is adapting to Ginsburg’s absence, but also signal its appetite for taking on hot-button issues during a politically charged time in Washington and the country.

Even with an expanded conservative majority, a number of experts on the court say its conservative members may have very different attitudes about how quickly the court should confront contentious issues.

The court’s most conservative members — Justices Clarence Thomas and Samuel Alito — may feel emboldened by the expected arrival of another like-minded justice and be more inclined Tuesday to agree to hear politicized disputes. With a newfound confidence that they have the votes to build bulletproof majorities around conservative rulings, they may vote in favor of taking up cases involving gun rights, labor union power and voting restrictions.

“You’d expect justices who have been champing at the bit on certain issues like guns, affirmative action or abortion would be more likely to want to get some cases in the hopper and put some pressure on Amy Coney Barrett right away,” said Robert Tsai, a law professor at American University. He added: “She might want to get her sea legs at first and avoid being on the record on certain things like abortion.”

Thomas and Alito are also seen as likely to be the least bothered by the prospect that an aggressive approach might undermine the court’s image as an apolitical body.

Chief Justice John Roberts, an institutionalist, is sensitive to perceptions of partisan influence over the court.

At its gatekeeping stage, the chief justice has some procedural tools he can use to steer the court away from embracing a highly politicized docket. One source of leverage is Roberts’s control over which petitions the justices will discuss at their regular meetings, known as conferences.

It’s possible that Roberts has already exercised this prerogative on the issue of abortion. Prior to Ginsburg’s death, the justices were slated to discuss whether to take up a restrictive Mississippi abortion law that would ban abortion after 15 weeks. But four days after Ginsburg’s death, discussion of the abortion petition was postponed to an unspecified later date.

During conferences, Roberts also gets to speak first about a petition, which could give him the opportunity to frame a disfavored case as being the wrong vehicle to address the legal issue at hand, explained Ben Johnson, a professor at Penn State Law.

“Plus, he votes first, which sends a signal to other justices,” Johnson said. “The remaining four conservatives could vote as a bloc and put the case on the docket, but they’d have to run the table after the chief told them this was a bad idea.”

Of the court’s five-justice conservative wing, the behavior of Justices Neil Gorsuch and Brett Kavanaugh, Trump’s two previous nominees and the most junior members of the court, were seen as the most difficult to predict.

Some legal experts say that, on balance, they expect the court to shy away from explosive issues in the near term, especially while Barrett’s Senate confirmation hearing plays out over the coming weeks.

“I would expect the court to refrain from taking on ‘hot button’ issues which will keep it in the headlines after the inevitably contentious hearings,” said Bruce Ackerman, a professor at Yale Law School. “Rather than further provoking political polarization over its role, it (will likely) defer serious consideration of high-visibility issues until after the election.”

Brianne Gorod, chief counsel at the progressive Constitutional Accountability Center, said the long-term trend could tell a different story though, especially if conservative legal groups see new opportunity in the 6-3 conservative court.

“There could certainly be consequences in terms of the justices’ decisions about which cases to hear,” she said, “and, on top of that, what cases parties decide to bring to the court.”