After their move to the forty sixth base, Nine had drilled one idea into their heads. As Valkyries, there was only one man they were allowed to have an intimate relationship with and that's the Doctor.
The new Head General was a charismatic man with many achievements to his name. It was through his efforts that they were able to end the war with the Nephilim, and even now he is working to ensure they have a future where they aren't treated as disposable war machines. Eleven saw the way he interacted with his Valkyries, and though he was much more stoic and lacking in energy, he reminded her of the Producer.
Though she understood why Nine and the others felt that way about him, the blue haired idol wasn't interested in the position of the Doctor's personal Valkyrie at all. That said, when she considered the idea of being the Producer's Personal Valkyrie, a violent inferno blazed inside her chest instantly heating up her entire body.
