Clara’s characterisation in Deep Breath is one of her strongest yet, but it also builds on nearly a series of writing which gave us plenty of insight into who she is and who she wants to be. One striking example is how her acceptance of the regenerated Doctor is handled. What changes her mind is that he needs her and that fits Clara’s character perfectly.
She strives to help other people, whether she is running after a child she doesn’t know in The Rings of Akhaten or staying as a nanny with the Maitlands after their mother dies. It’s not merely selfless dedication, she likes it when other people depend on her. “And best of all, he really needs you”, she says about the Eleventh Doctor.
And so he does not, in fact, guilt her into continuing to travel with his future regeneration - but asks her to help. Because that is what Clara Oswald does.
"Why this one? Why did I choose this face? It’s like I’m trying to tell myself something. Like I’m trying to make a point. But what is so important that I can’t just tell myself what I’m thinking?”
You can’t see me, can you? You look at me and you can’t see. Do you have any idea what that’s like? I’m not on the phone, I’m right here. Standing in front of you. Please just… just see me.
“SS Marie Antoinette. Out of control repair Droids, cannibalizing human beings. I know this is familiar, but I just can’t seem to place it. Sister Ship of the Madame De Pompadour. Nope, not getting it.”
And when you gaze long into an abyss the abyss also gazes into you.