A former contestant on Donald Trump’s “The Apprentice” said Friday that the Republican presidential nominee forced himself on her at a meeting at a hotel in 2007, kissing her aggressively, touching her breast and thrusting his genitals toward her.

Summer Zervos, who appeared on Season 5 of the reality show, became the latest woman to come forward with allegations of unwanted sexual advances from Mr. Trump since last week’s release of a video showing Mr. Trump in 2005 speaking lewdly about being able to force himself on women...