Pot it up with a good potting soil in a 1G nursery container (plant deep) and let it grow on for the rest of the season. Before really cold weather comes on, sink the pot into a loose soil, well-drained area of your garden and mulch well.

You could plant it out next spring but I find those packaged roots often need a bit more TLC than just a single season can provide. Personally, I'd wait to plant it in its permanent location until next fall, when the roots should have filled the container. btw, there IS some green growth on it now, isn't there?

No, there's nothing green about it...looks like a dead root. Is there any hope it will grow?

If it looks like a dead root, it most likely IS a dead root. Sorry :-( Bare root starts of clematis are just difficult to establish at even the most ideal time of year (late winter/early spring) but if they haven't had any attention at all, they are essentially garbage by this time of year.

But.......clematis can often offer some very surprising activity, coming to life after an extended period of inactivity. As you have nothing to lose, you might as well just go ahead and proceed as if it were alive and see what happens next spring. Stranger things have happened.....:-))