WASHINGTON — The Supreme Court dismissed on Tuesday an appeal in one of the cases challenging President Trump’s efforts to limit travel to the United States, calling an earlier version of the ban moot because it has expired.

That travel ban has since been replaced with broader restrictions, and a second case remains before the justices — but it is likely to meet the same fate. If it does, a politically charged clash between presidential power and claims of religious discrimination that could have produced a blockbuster decision will instead end with a whimper.

A new wave of litigation aimed at Mr. Trump’s latest policies, announced last month, is already underway, and appeals in those cases may yet reach the Supreme Court. For now, though, what could have been one of the marquee cases of a busy term was removed from the docket.

The case the court addressed Tuesday came from the federal appeals court in Richmond, Va., which had ruled that the earlier travel ban, issued in March, violated the Constitution’s protections against religious discrimination by singling out travelers from six predominantly Muslim countries.