If it's pot grown...anytime of year providing it is kept watered, if you want to plant a bare root plant (dug up from a field or moved from one place to another), best time is when the plant is totally dormant...ie has lost all its leaves so in the next few months.
Enter "clematis" in the Category Search option to the left and you'll find numerous references to cultivating clematis. Especially look at the one titled "droopy clem"... Good luck...
A clematis Montana grown in a container can be planted almost any time BIRD, except in the height of summer or the depths of winter. Now is fine. Do make sure that its roots are in the shade and the stems will be in the sun. We've had ours about 15 years and lightly trim it back after the May flowering has finished. Of course you won't need to bother with a new plant, but if it's happy it will grow and grow,and grow....a fabulous choice.