Numerous NPC diplomats, ambassadors, and a few named senators from the Galactic Republic (including Senator Arnus) wear this tailored suit and cape. The suit is always in neutral colors like gray, tan, or drap. Some have a sunburst symbol over the left side of the chest. Some only have kama-style capes over the lower back, while others have a single-shoulder cape secured by a thin cord over the left shoulder. Some capes have gold trim and diagonal stripes, while others are plain colored. These capes and sashes are most often deep blue, red, brown, or green. This generic outfit closely resembles the Corellian Councillor uniform, which uses tan, red, and brown colors.
For a closer look at the details, Jedipedia has great 3D turn-around of these NPC costumes under the “Diplomat” and “Ambassador” search terms. These characters can be found on Coruscant, Voss, and in Republic spaceports across the galaxy.
Although the video game only uses male models for this costume, the Galactic Senate welcomes costumers of all genders to make this outfit.