The list of cases pending on the Supreme Court’s calendar this year lacks blockbusters, but court watchers say they are hopeful some of the big ones are added before the end of the term.

The justices convene their 2018-2019 session Monday with far more drama over who will be the ninth member of the court than over the cases on the schedule.

October’s cases include a fight over property rights, whether a death row inmate can be executed if he can’t remember committing the crime after a stroke, and the extent of the Endangered Species Act and unoccupied private land.

All sides are hoping the court will be ready to accept some of the more consequential issues percolating in the lower appeals courts once a ninth justice is confirmed.

Options include gay rights in the workplace, transgender rights in the military, the legality of President Obama’s Deferred Action for Childhood Arrivals deportation amnesty and President Trump’s attempted phaseout of the program, the drawing of congressional districts ahead of the 2020 census, and abortion rights for illegal immigrant teens.

“The real key to the coming term is what is in the pipeline,” said Noel Francisco, the solicitor general.

The court could be suffering a hangover from its term that ended in June. Mr. Francisco called it the most consequential term in years, with decisions upending 40 years of precedent on mandatory union dues, legalizing sports gambling across the nation and upholding President Trump’s travel ban.

The term also ended with Justice Anthony M. Kennedy’s retirement after three decades.

Justice Kennedy was considered a swing vote on cases involving how congressional district lines are drawn in states and how much of a role politics can play.

The court last year sent several such cases back to lower courts for more development.

One of those could soon be back.

“A big one to watch is a North Carolina case that could bring the question of the constitutionality of partisan gerrymandering back to the court,” said Brianne Gorod, chief counsel at the Constitutional Accountability Center.

Another case working its way through lower courts involves whether Title VII of the Civil Rights Act protects gay employees from workplace discrimination.

Lower courts have traditionally ruled that gay rights aren’t part of sex discrimination as envisioned in the law, but a handful of appeals courts have ruled that the law does in fact cover LGBT claims from employees who say they were fired because of their sexual orientation.

Presidential powers could be tested as the Trump administration, Republican-led states and immigrant rights advocates battle over Mr. Obama’s 2012 DACA policy granting tentative legal status to illegal immigrant “Dreamers,” and Mr. Trump’s decision last year to phase out the program.

One district judge has ruled the original Obama-era DACA illegal, but several other courts have ruled Mr. Trump’s attempt to phase out DACA as illegal.

That has left a legal minefield that is being debated in several appeals courts and could reach the justices.

The Trump administration is also facing a legal battle in the U.S. Circuit Court of Appeals for the District of Columbia over whether the federal government must facilitate abortion services to illegal immigrant minors.

Judges heard oral arguments in that case last week.

None of these cases is guaranteed for this Supreme Court term.

One case the justices have agreed to hear is that of a Pennsylvania woman whose 90-acre farm might hold a centuries-old cemetery. Rose Mary Knick claims a Scott Township law giving the public some access to cemeteries is an abuse of her private property rights.

She brought her battle to state court, arguing that Scott Township can’t take her property without just compensation, but the court dismissed her case because she hadn’t been fined.

Ms. Knick argues that she should be able to take her case to federal court without having to wait for a state court to hear her property challenge against the local government.

Ilya Shapiro, a senior fellow at the Cato Institute, said the case will go a long way toward telling future plaintiffs where to fight their property cases.

“This is unusual because no other constitutional right works this way,” he said, adding that Second Amendment challenges go straight to federal court.

Criminal defense cases always loom large on the court’s docket, and one for this term involves a man who has served his sentence for a heroin-dealing conviction but is challenging the state’s attempt to forfeit his Land Rover. He purchased the vehicle with an inheritance and used it to commit his felony offenses.

Lower courts ruled that the state’s action in taking his vehicle, which was worth more than the fine the man faced, violated the excessive fines clause under he Eighth Amendment.

The Indiana Supreme Court disagreed and allowed the forfeiture.

Parties including the Chamber of Commerce and the American Civil Liberties Union are backing the ex-convict.

“This case may be an issue where liberals and conservatives agree on a pro-criminal-defendant case,” said Josh Blackburn, a professor at South Texas College of Law.

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