Judyg - Thank you just deleted other post. The leather a dark brown. The walls are a light creamy neutral with white trim. The color in the rug is actually a black.

How would this drape look with your rug and wall color? It has some of everything, including the white of your trim in the Greek key trim. These, if the colors work, would be great with the leather, too.

I thought your might be interested in this ideabook
https://www.houzz.com/magazine/8-secrets-to-pairing-patterns-with-an-oriental-rug-stsetivw-vs~3794334

judyg - love those curtains and would certainly look good.
doultcolt1 &sam0705 - love the suggestions. I'd like to stay within the neutrals but add color. I'm not exactly crazy about the red in the rug and didn't know if there is a way to tie in or add another color. The majority of the red in the rug will be covered by coffee table. Do you think its possible to add a color in that is a little more "light and airy" looking? The rug was a gift and I cant replace it at the moment so really trying to add accents, pillows & etc around it.

I think you'll see in that ideabook that you don't have to be perfectly matchy with the rug. Do I see some sage green or light blue in there? Those could be colors to pull out for a lighter look to balance out the maroon you don't like. If adding throw pillows or drapes (and I like the ones judyg has suggested) I would try some larger graphic patterns or a wide stripe. I think it will help modernize the space a little bit so it's not too traditional with the rug.
I am attaching my favorite living room on houzz. If this is something you like, you could consider layering a shag rug over your current rug for a lighter look. I did this with a red oriental rug in my kids' play room and I love it.

Try a gray,. SW Special Gray or Repose Gray would be nice. Gray always looks great with maroon.

A piece of art that you love, preferable on canvas which incorporates all the colors in your rug...the least is the red. I would pretty much ignore the red. Concentrate on the neutrals you want, just make each addition special...as, the burlap fabric, rough, works with the leather, smooth, and the trim with the rug and the your woodwork. Lamps, just different enough, so attention is focused on those, too.

Something on the coffee table...maybe in black pottery. Look in the products section here and post some of the things you like.

You can pair contemporary art with this type of rug...I have three of these types of rugs in my great room...huge rugs over hardwood floors and lots of colorful contemporary art...it looks great!

I like the curtains Judy suggested as well. Maybe a gold in the pillows on your couch with a ikat pattern or other geometric shape to keep it fun. Lampshades could bring in a pop of color as well.

To find colors that go with your rug, first find paint chips that perfectly match the rug's colors. Then, on the paint strip where you found the matching color, go up or down and choose lighter and/or darker versions of it. Any of these will be candidates for colors of fabrics or accessories and will 'go' with the room. Since you want light and airy, choose more of the lighter versions but don't be afraid to use a little of the darker. Every color you choose from the same strip (even if you pick 6) will count as one color added to your room, because they are all the same hue, just different tints and shades of it. You can also pick the chip and then find its complementary color on the paint company's website.
Once you have these chips in hand, take them with you when shopping for items. Good Luck, love your rug!

I suggest that you paint the walls the color of the draperies that Judyg suggested. I think the walls should have the same richness as the rug to balance and ground it and going with a wall color that's too light won't accomplish that. Beautiful rug!

What you really need to do is photograph your rug and pull colors from it to find color inspiration. I created a app called Color911 for instant color help. One of the features is to take a photo and pull the colors from the photo. I attached a screen shot from the app showing when I took a photo of a rug and pulled the colors from it. What I've done is used those colors for wall color, accent colors.. or just inspiration for anything else I am buying for the room. To match the colors to paint simply take your iPhone or iPad to the paint store and they can find a paint color to match. I have done it several times. This is an incredibly useful feature. I hope this helps you with the design for the rest of your room!