One light fixture is not going to make your space look more modern.

I think what you are picking up on that is leading you to think of replacing the light is how dark the gray paint and wood wall have made your room. a room of this size without many windows would really benefit from bright white paint instead of both elements.

I think a new flush mount fixture would be beneficial in your small space. Look for a fixture that has three or four light bulbs. That way you have a lot of options with bulb wattage and amount of light the fixture puts out. Also look for a fixture that has an opaque shade so you don’t see the bulbs. Here is a quatrefoil 3-light and a star 4-light:

Agree with Jenna that the paint isn’t doing you any favors. And it seems to clash with several features of the room.

Absolutely uodate the lighting. Get a nice hanging fixture for above the table and another off to the right. The one on the right should be flush-mount.

I might put in a track light of sorts this would let you get the light places.. im not mad at your paint color but the room was already pretty dark. as a side not art should be at eye level as well as that small mirror.