Summer Zervos, who starred in the 5th season of ‘The Apprentice’, filed a lawsuit against Trump in New York state court this January. She claims he defamed her character, and knew his supporters would subject her to threats of violence:
Zervos, represented by Gloria Allred, claims that Trump tarnished her reputation by denying acts boasted to Access Hollywood's Billy Bush about grabbing women's genitals. The Apprentice alum accuses Trump of kissing her twice in 2007 and attacking her in a hotel room. In response to this, Trump put out a statement that he "never met [Ms. Zervos] at a hotel or greeted her inappropriately," along with tweets how his accuser "made up events THAT NEVER HAPPENED." — Hollywood Reporter
The full text of Ms. Zervos’ complaint described the incidents:
Summer Zervos is one of many women who has been subjected to unwanted sexual touching by Donald J. Trump. By his own account, Mr. Trump engaged in such assaultive behavior repeatedly, and with immunity [...]
Ms. Zervos was ambushed by Mr. Trump on more than one occassion. Mr. Trump suddenly, and without her consent, kissed her on the mouth repeatedly; he touched her breast, and he pressed his genitals up against her. Ms. Zervos never consented to any of this disgusting touching. Instead, she repeatedly expressed that he should stop his inappropriate sexual behavior, including by shoving him away from her forcefully, and telling him to “get real”. Mr. Trump did not care, he kept touching her anyway.
Trump’s lawyers are now arguing that this lawsuit should be dismissed, or deferred till Trump leaves office. They’re arguing the constitution grants the president broad immunity from lawsuits that could “distract a president from his public duties” (aka, prevent him from tweeting):
"Moreover, as in Clinton v. Jones, the public interest mandates that the immunity issue be resolved before proceeding further," writes Kasowitz. "The 'singular importance of the President’s duties' warrants a stay where civil actions, such as this one, 'frequently could distract a President from his public duties, to the detriment of not only the President and his office but also the Nation that the President was designed to serve.' Requiring President Trump to litigate the merits on a motion to dismiss the complaint, in addition to moving to dismiss on grounds of Presidential immunity, would negate the very interests that that immunity is designed to protect." — Hollywood Reporter
Of course, the Supreme Court has heard a version of this claim. It ruled in Clinton v. Jones that the president has no immunity from civil litigation for acts done before taking office and unrelated to the office of the presidency:
Petitioner's principal submission--that in all but the most exceptional cases, the Constitution affords the President temporary immunity from civil damages litigation arising out of events that occurred before he took office--cannot be sustained on the basis of precedent. [...]
The separation of powers doctrine does not require federal courts to stay all private actions against the President until he leaves office. [...]
The Court is not persuaded of the seriousness of the alleged risks that this decision will generate a large volume of politically motivated harassing and frivolous litigation and that national security concerns might prevent the President from explaining a legitimate need for a continuance, and has confidence in the ability of federal judges to deal with both concerns. If Congress deems it appropriate to afford the President stronger protection, it may respond with legislation. — Findlaw
That decision was 9-0 against then President Bill Clinton.