It will likely be a new character, continuing the tradition. As for what kind of character, likely someone in Tevinter or possibly Seheron. A human of any class, from soporotti to altus. An elf of any status, from slave to initiate. Even a dwarf could make an appearance, as Tevinter deals with dwarves all the time for lyrium. A qunari would be tricky to implement. They would have to be either Vashoth or Tal-Vashoth. I don't see a Qunari working toward anything other than Tevinter's destruction. But even Vashoth would have difficulty moving about in Tevinter. Maybe if the game revolves around covert operations then it could work.
I just don't see what the (ex)Inquisitor plans to do in Tevinter. Find some useful people Solas doesn't know, okay. Steal acquire information on magical items, the Veil, elvhen history? Investigate certain sites where elvhen temples may have been built over just in case those hold information? Then what?
I think MY Inquisitor's first order of business would be finding a way to block petrification. Next, find the Hero and the Champion. The cure won't be of any use if the entire world is destroyed (though the cure was likely found by now), and the status of the Warden Order won't matter either. Try to contact Valta. If her titan was upset just by the Breach, then it will be in for a major shock if the entire Veil drops. Work with the auger of Stonebear Hold and the spirits to see if they can learn more about the Crossroads dimension and the nature of the Fade. Have the Divine (Vivienne) work with the mages to prepare them mentally and emotionally for what might come, as I suspect they will be desperately needed if the Veil falls. Also have them research ways to strengthen the Veil or emanate its same magic, or how to strengthen the real world's composition against the magic of the Fade.
This is another place where Trespasser messed up. The alliances with Orlais and Ferelden are needed now more than ever, and those countries need the Inquisition as well to coordinate the effort.