* Senate has refused to act on Obama nominee Garland
* Court's term starts Monday, runs through next June
* Religious rights, insider trading, trademark fight on tap
* Transgender, voting rights cases could be added
By Lawrence Hurley
WASHINGTON, Sept 30 (Reuters) - The U.S. Supreme Court opens its new term on Monday in uncharted territory, with an vacancy on the bench on a presidential Election Day now certain for the first time since Abraham Lincoln won re-election in 1864 at the height of the Civil War.
While the eight justices will start to hear oral arguments on a range of issues including religious rights, insider trading and intellectual property, attention will be focused on the Nov. 8 presidential election that will determine who will get to replace Justice Antonin Scalia, who died on Feb. 13.
In Lincoln's time, Chief Justice Roger Taney, author of the notorious pro-slavery Dred Scott decision, died in October 1864, just weeks before the election. After Lincoln won re-election, he appointed the anti-slavery Salmon Chase as chief justice in December 1864. That tipped the ideological balance of the court in Lincoln's favor, according to legal historian Paul Finkelman, who teaches at the University of Saskatchewan College of Law in Canada.
In a step with little precedent in U.S. history, the Republican-controlled U.S. Senate has refused to consider confirmation of appellate judge Merrick Garland, President Barack Obama's nominee to replace Scalia, saying the next president should make the appointment. Obama's term ends on Jan. 20. Congress is now in recess until after the election.
More than 150 years after Lincoln appointed a new chief justice, the next appointment could similarly herald a major shift on the court. Without the conservative Scalia, the court is split with four liberals and four conservatives, after years of conservatives in the majority.
If Scalia is replaced by a more liberal justice, "we would see a five-vote solid, consistent liberal majority that could write its own ticket on a lot of issues," said conservative legal activist Carrie Severino.
The court could tilt to the left on issues such as gun rights, voting rights and the death penalty, among others.
In the next president's first four-year term in office, there is the chance of filling even more vacancies. Three of the justices are 78 or older: liberal Ruth Bader Ginsburg (83), conservative Anthony Kennedy (80) and liberal Stephen Breyer (78).
Democrat Hillary Clinton faces Republican Donald Trump in the election. Some Republican senators are concerned that, if she wins, Clinton could nominate a justice more liberal than Garland, raising the possibility the Senate could move to confirm him after the election and before Clinton is sworn in. But the Senate's top Republican, Mitch McConnell, has said he has no plans for that.
In the meantime, the court will proceed shorthanded into the 2016-17 term that runs through June, hearing arguments and issuing rulings, with Chief Justice John Roberts' court likely eager to avoid taking up cases that could lead to 4-4 split decisions.
Such rulings leave in place lower court decisions and provide no national legal precedent. Four cases last term ended in 4-4 splits. One was in one of the court's biggest cases: Obama's failed bid to revive his plan, blocked by a lower court, to protect millions immigrants in the country illegally from deportation.
One way the court can try to avoid divisions is to take up issues on which the justices are not ideologically divided.
There are already signs the justices are doing so, as shown by an uptick in intellectual property disputes they are hearing, including a major design patent battle between Apple Inc and Samsung Electronics Co Ltd, which will be heard on Oct. 11.
Cases on transgender rights and Republican-backed state laws that opponents contend were designed to suppress the turnout of black, Hispanic and other voters who tend to back Democrats potentially could be added to the docket, although those cases could lead to 4-4 ties.
The court on Thursday took up eight new cases, including another intellectual property fight over whether the Oregon-based Asian-American rock band The Slants can trademark its name despite the term's history as a racial slur.
Among other cases of note, the court on Wednesday will consider Illinois businessman Bassam Salman's appeal of his insider trading conviction in a case that could hem in prosecutors in bringing such charges in the future.
On Election Day, the court will consider a case that touches upon race discrimination and predatory lending. The justices will decide whether to allow the city of Miami sue Bank of America Corp and Wells Fargo & Co over their lending practices.
The court has not yet scheduled oral arguments in a religious rights case it agreed to hear before Scalia died. It concerns whether Missouri, on the basis of the constitutional precept of separation of church and state, can exclude a Lutheran church that operates a daycare center from a state program that awards grants for resurfacing playgrounds.
Some Supreme Court experts say the court may be waiting until Scalia's replacement is seated before it hears the case because it may divide the court along ideological lines.
Reporting by Lawrence Hurley; Editing by Will Dunham