Ms. Kelly is viewed by some TV veterans as a vehicle for the network to turn from the hard right tone Mr. Ailes established to a more centrist approach.

“If they are going to make a network that is going to be a post-Ailes/post-Trump, it will be around Megyn Kelly, Chris Wallace and Shep Smith, and they are going to have to throw Hannity and O’Reilly overboard,” said Andrew Tyndall, a television-news consultant, of other hosts at the network.