Well, my canon Inquisitor, while not power-hungry per se, has absolutely zero faith in the other institutions of Thedas. If you want something done right, you've got to do it yourself. Thus her post-DA:I actions would largely be concerned with the consolidation of power.

In no particular order: *Increase trade as much as possible. Now that people are not relying on the Inquisition for fighting anymore, make them reliant on us for trade. *Keep pressure on Orlais. Gaspard, Briala and Celene are all still around and at each other's throats. Use this to force Celene into pushing social reform, particularly for the elves. * Negotiate with Orlais, and possibly Ferelden, for the surrender of land to the Inquisition around Skyhold. Begin the construction of a trade village outside of the Skyhold fortress. *Establish cities around Inquisition bases. Reinforce with troops. These bases are part of the sovereign entity of the Inquisition, not the nations in which the reside. *Encourage trade with the Dalish. Offer them the possibility of settlement on Inquisition lands. *Start seizing as many elven ruins as possible. Obviously Cory was on to something when messing around with elven magic. *Research the elven artifact we have (such as the eluvian and the orb); try to find a way to use their magic. Tracking down Solas and squeezing all his knowledge out of him falls under this bullet point. *Continue tracking down red lyrium and destroying/confiscating it. *During all of this, keep up aid for the impoverished and disenfranchised in all nations the Inquisition has a foothold in. Make sure the people retain a sense of thanks and indebtedness for the Inquisition. *Set up mage schools on Inquisition lands/in bases. Within these schools mages are free to come and go, families are allowed to stay with their children, and templars live alongside them in case of emergency. Friendship between templars and mages is encouraged. *Begin weaning all of the Inquisition's templars off lyrium. *(Not for certain) Invade Tevinter with the goal of overthrowing the institution of slavery, possibly after encouraging The Divine to declare an Exalted March upon them. If the Magisters capitulated to the Inquisition's demands, the invasion would stop and the Inquisition would begin humanitarian efforts to provide relief for the former slaves and war-torn areas.