Allison Gollust, who led marketing at the network, had remained in her job after she and Mr. Zucker, the former president of CNN, acknowledged a romantic relationship.
Inside the media giant, unease has been mounting: over the network’s corporate ownership, the firing of Chris Cuomo and a looming merger with Discovery.
Chris Cuomo and Mr. Zucker, the former CNN president, are among those whose careers have suffered in the year since the former governor was first accused of sexual harassment.