The picture link I sent; that animal was harvested about 2 miles from where a grizzly ate some guys skidoo seat. There was blood on the seat from his hunt and the griz was hungry. The bear was shot in Yellowknife city limits by a resources guy about a week later. Usually the grizzly bears stick to the tundra about 120 miles north of Yellowknife, but this one was sick, hungry, had bad teeth and followed the caribou down with their migration.
Usually, there is no chance of seeing grizzly in the Yellowknife district, but like the freak incident in Nov. 2004 there is the minute possibility. If you are lucky, you may see a few wolves, or maybe the odd black bear, but not a grizzly.
I am not sure about "trophy fees" in Quebec, but the NWT has pretty steep fees to bring trophies out of the territory. They are listed with the license fees. Make sure you factor in that cost when you consider going to Yellowknife.
YKD