WASHINGTON—The Supreme Court on Tuesday agreed to consider an appeal by Visa Inc., MasterCard Inc. and several leading banks that are challenging lawsuits alleging they conspired to set anticompetitive ATM fees.

The case was one of eight new matters the court added to the docket for its next term, a move that will help give the court’s coming calendar more heft. The court has been operating with eight members since the February death of Justice Antonin Scalia, leading to a dynamic where it has been slow to take new cases and...