Art brushes will not "overlap" or "close" upon themselves. You essentially can't get rid of that "gap". That is not how Art Brushes function. You may notice that even the default Art brushes in Illustrator show this beginning/end.
If you want to remove the "gap" you need to use some other method than an Art Brush, or break the circle and cause it's path to overlap upon itself (not my personal recommendation).
If you aren't seeking to have end caps...
You can square-off the ends of your artwork and use the "stretch between" option for the Art brush.
A Pattern Brush may be more fitting.
It's how they are intended to work - note in my screengrab the similarity between the preview in the brush palette and the highlighted stroke within the applied brushstroke - the preview shows you explicitly the relationship between underlying spline geometry / control points and the applied brush.
If you want to avoid those gaps, my best advice is to make a new art brush yourself with either square or half-rounded ends, but the textural body you wish between those ending elements, and set the brush to stretch between Guides, and set the guides at the start of each of the ending areas - that way when you overlap those ends, they visually merge in a way which is pleasing - but only if you actually overlap your path - as you can see in my screengrab, I had to overset the anchorpoint of one end past the other to get a smooth transition - just using rounded ends and guides didn't do it.
Scott's answer of squared ends and guides will work for when your path will be closed fully - my rounded ends will work when you wish y our paths to intersect in a visually pleasing manner.
Hope this helps.