A founder of the Sundance Film Festival is expected to go to prison for at least six years after he pleaded guilty in a Utah courtroom on Tuesday to molesting a young girl. The case came to light after he was recorded apologizing to a man he admitted having groped more than 25 years ago.

Sterling Van Wagenen, a director who helped establish what became the country’s most prestigious annual film exhibition, pleaded guilty in Utah County to one count of aggravated sexual abuse of a child. His lawyer, Steven Shapiro, said Mr. Van Wagenen planned to plead guilty to an additional count, involving the same girl, in neighboring Salt Lake County on Thursday. As part of a deal with prosecutors, Mr. Shapiro said he is expected to receive two sentences of six years-to-life in prison that he will serve concurrently.

Mr. Van Wagenen, 71, was charged with molesting the girl on two occasions between 2013 and 2015, when she was between 7 and 9 years old. But this was not the first allegation against him.

Sean Escobar, who as a boy was friends with two of Mr. Van Wagenen’s sons, said that Mr. Van Wagenen had touched his genitals during a sleepover at the director’s house in the early 1990s.