I see that not a single one of you seem to think that Jaime will retain his position. I'm convinced that Dany as queen would keep Jaime as LC, now before you all jump up and call me crazy let me explain.
Jaime killed Aerys, but as Dany learns more and more about her father, and the atrocities he committed, she will accept the fact that Jaime did the right thing. Dany is her fathers daughter, she too has committed atrocities, but always with good intentions. At some point she will cross a line and take things to far. She'll do something that will haunt her wether it's burning a city of innocents alive because their lord refused to kneel, or executing families (including young heirs) as revenge for the sack of King's Landing. At some point she'll come to realize how easy it is to abuse her power, how easy it would be to become a Mad Queen.
Now we've seen Maggy the Frog's prophecies slowly come to fruition, so the odds of Cersei being Killed by the Valonqar are pretty high. This means she not likely to lose her trial, and have her will freedom when Dany and her army arrive. We know she is willing to kill herself, her children, and other members of the nobility if the city seems likely to be overrun. We saw this in the Sept during the Battle of the Blackwater, when she was ready to turn the Sept of Baelor into Jonestown.
We know about the wildfire, Cersei knows about the wildfire. I believe that when Dany comes to take the throne Cersei will hold the city hostage, under threat of following through with Aerys plan. At this point, once again Jaime will be the only one willing to do the right thing, and become both King and Queenslayer.
Dany knows how easy it is to cross that line. Jaime will have proven twice that he won't let that happen. She will keep Jaime close, sword ever ready, to stop her when/if the time comes.
Note: my theory kinda relies on Jaime being the Valonqar, and if Aerys+Joanna=Jaime/Cersei it works even better as Jaime retaining his position would remove him as a claimant to the throne....
