Either turn the rug 90 degrees, or get a larger one. Get fabric or readymade curtain panels for doorway to closet. You could use a tension rod for an inside mount, or treat it like a window and put a decorative rod mounted outside of the door trim. Grommets will allow the curtain to slide very easily and push out of the way.

I would rather use a roller blind than a curtain. grey with some nice texture.

also that bench looks lonely . check out this entry http://sainteriordesignstoronto.com/back-to-basics.html

Thanks for the comments I will add a curtain probably using tension rod idea & I'm fed putting something over bench, just trying to get curtain and rug looking right in the space! If u have any pics of suggestions or ideas pls post! Thanks again :)