[ He's done what he hoped to do, now he needs and wants to address the turmoil she's clearly feeling. He would take it from her if he could. He could, technically, but this is an entirely different situation.

As she clings to him, the Doctor's arms shift to pull her close, holding her now in a far different way than their previous hug, with one hand resting against the back of her head. This is protective, an embrace of knowing, without the words needing to be said. Something was shared between them and he knows just enough about the future to understand what she may have seen. He doesn't like it, at all. She shouldn't have to carry this burden. ]

Secrets can keep us safe, but they aren't easy to bear. Sometimes we have to, for the sake of everything, I know that, but you specifically, shouldn't have to, not for my sake. I'm sorry.

[ He only saw a glimpse, but it's enough to infer. He knows he dies and regenerates (which he shouldn't be able to do), it's only the details he's clueless about. And there are a lot of details in the mix there. ]

I'm not going anywhere today, or tomorrow, or even the next day.

[ He has a big showy speech in mind for all of this, but right now it just feels like the only thing to say, the only thing he really can say. ]