Megyn Kelly’s new office at NBC News sits a block north of Fox News headquarters in Midtown Manhattan. But it might as well be a world away.

In switching networks at a pivotal point in her career, Ms. Kelly, the No. 2-rated personality in cable television news, is taking a calculated risk that she can swap her dedicated Fox audience for the broader, but more fickle, viewership of network television.

There are challenges from the get-go. Her splashy arrival has the potential to fray nerves among the big personalities at the network — who already compete against one another for interviews and scoops. Ms. Kelly, 46, will also be taking on a daytime talk show format that has been a virtual graveyard for television news personalities in the last 10 years.

And the new Sunday newsmagazine show that NBC plans to build around Ms. Kelly will go up against a giant that has not been meaningfully challenged for decades: “60 Minutes” on CBS.