The Supreme Court kicked off its new session Monday morning, with Justice Neil Gorsuch on the bench for his first full term and the justices immediately diving into a hot-button labor dispute.

Numerous other challenges are on the docket for this term, covering everything from religious liberty to union dues to voter redistricting. Consideration of President Trump’s controversial travel ban is on hold, though the issue nevertheless looms over arguments.

But first up Monday was a clash between businesses and employees, focused on how workers can complain about pay, conditions and other issues. In a rare split, the dispute pitted Justice Department lawyers against those from the National Labor Relations Board.

At issue are contracts employers want to enforce that prevent workers from pursuing group claims in court. The case involves workers who tried to sue a Murphy Oil USA gas station in Calera, Alabama, but had contracts requiring any dispute be settled in individual arbitration.

Employees say going it alone is too costly and makes it impossible to pool resources for a lawyer.

Lower courts have split over whether the agreements are enforceable. And so have federal agencies.

The NLRB originally had found the requirement violates federal labor laws. But the Trump administration reversed the Obama administration's position in support of the NLRB.

The result is that government lawyers representing the Justice Department and the NLRB opposed each other in court Monday. While the Justice Department contended the businesses should win, the NLRB argued the workers should be protected.

Judge Neil Gorsuch shakes hands with Supreme Court Associate Justice Anthony Kennedy after being sworn in as an Associate Justice of the Supreme Court, accompanied by Louise Gorsuch (C) and U.S. President Donald J. Trump in the Rose Garden of the White House in Washington, U.S., April 10, 2017. REUTERS/Carlos Barria - RTX34YQB (REUTERS)

Justice Ruth Bader Ginsburg said earlier she's never seen such a split in nearly 25 years on the high court. During arguments Monday, Ginsburg seemed to speak for the court's liberal wing, saying the importance of collective action is "there is strength in numbers. You have to protect the individual worker in a situation where he can't protect himself."

But Chief Justice John Roberts sounded concerned about a ruling for the workers, which he said "would invalidate contracts for 25 million employees." That's the estimated number of non-union workers who have contracts with the individual arbitration provision.

Unlike last October, the justices convened Monday with a full bench, after Trump earlier this year installed Gorsuch to fill the vacancy left by Justice Antonin Scalia’s death.

One high-profile case could disappear, at least for now. The court canceled the Oct. 10 argument over Trump's travel ban after the president announced a new policy last week that differs from the one the justices had decided to review.

Still, many important cases remain that touch on gay rights and religious freedoms, the polarized American electorate, the government's ability to track people without search warrants, states' rights to allow betting on professional and college sporting events and the ability of labor unions that represent government employees to collect "fair share" fees for contract negotiations from workers who don't support the unions.

And speculation has not receded over another possible vacancy in the near future.

Sources close to Justice Anthony Kennedy say he has been seriously considering retirement and may not stay on the bench for Trump's entire first term. Rumors were at a blustery pitch that he would step down last June, but the new term begins with the 81-year-old justice on board, his unique power base intact.

His influence as the court's "swing" member -- the deciding vote on a range of high-profile cases from gay marriage to immigration to abortion -- has left his seat coveted by those on the right and left. Replacing him would launch an epic political fight, and could prove a boost to the Trump presidency itself.

For now, Kennedy's moderating presence could blunt the Trump agenda and that of fellow conservative Republicans. Other court watchers wonder about the plans of the liberal Ginsburg, at 84 the oldest member of the court.

Fox News’ Bill Mears and The Associated Press contributed to this report.