The Trailing Sectors was a region of the galaxy west of the Corellian Run, "trailing" the region known as The Slice.
Westward of the Corellian Run, Republic traders had business with Herglics, Grans, and Tynnans.
The Alsakan Conflicts and depredations by slavers and pirates who came outside of the Galactic Republic, caused devastation in the Expansion Region areas of The Slice and forced settlers in those expansion areas west of the Corellian Run. Prosperity pushed colonization into and beyond the Mid Rim.
It was further opened to settlement by the expansion of the Corellian Trade Spine and the discovery of the Rimma Trade Route followed by the Hydian Way.