The parent company of Fox News is standing by star on-air talent Bill O’Reilly in the wake of a news report detailing multiple settlements of claims of sexual harassment against him.

According to the New York Times, 21st Century Fox or Mr. O’Reilly have made payments totaling roughly $13 million to settle complaints made by women who worked as on-air contributors or producers during his time at the channel, which dates back to 1996, the year Fox News launched. Mr. O’Reilly is the host of “The O’Reilly Factor,” the news channel’s...