So who thinks it was the right move for Kirkman to keep Aaron as his chief of staff? I can see Kirkman's argument that he needs someone who can play the dirty insider political game Kirkman is a political novice but Aaron does not seem like a very loyal guy.
I think it was necessary and Kirkman realizes it. What he needs in a Chief of Staff right now is someone who knows all the players in Washington, not someone who had to spend time learning that as she goes. Aaron has that knowledge already, and in a crisis situation that's what Kirkman needs. His existing Chief of Staff was limited to knowing what affected Kirkman's old position, and that's it, so she probably didn't have that level of knowledge.
That being said, Kirkman clearly knows what kind of person Aaron is and is likely wary of him.
We saw the last scene where the woman hands him a folder on Kirkman, that Aaron is up to something.
It's possible that he could be up to something to undermine Kirkman, but I would like to offer a different take on that scene. Perhaps he was just trying to get a copy of whatever security clearance check Kirkman had to go through when he was appointed to cabinet, just so that Aaron could prepare for anything (good or bad) in Kirkman's past that might come up in interviews, etc.
He seems to me to be a very ambitious, opportunist guy who would backstab Kirkman in a heart beat to get ahead.
Again, possible, but where could he go to get ahead? He's already now the Chief of Staff to the President. Where else could he go from there? In fact, it's likely that if he did undermine Kirkman to the point where someone else becomes President somehow, they could bring in their own Chief of Staff and he'd be out of a job.
She seemed very dispirited after learning that she would not get the job. Who knows if it won't discourage her and lead her to go somewhere else?
Yeah, she was disappointed, but it's not like she's out of the loop. After all, she's now a special advisor to the President. As
Morpheus 02 said above, she could look into other things while Aaron is preoccupied with being at the President's beck and call.