That said I see a value to linking it to the original frontier so this is how I would do that:

The new frontier would border the Great Expsnse same as the old Frontier map 

The new frontier is "west" of the old frontier such that Tom Stephens expanded map's left hand edge abuts up against the new frontier's 3x3 map

This makes it possible for individuals to travel from one to the other but it's not easy and it's dangerous 

Also a while back I learned that a super nova would have the effect of irradiating Star systems for 120 LY in diameter so to the west of the New Frontier this happened (a super nova) and the edge of its 120 LY diameter radiation zone is the left or "west" edge of the New Zfrontier. This makes the area to the left or West of the new Frontier the "Badlands" irradiated system and the deeper you go in that direction the more radiation and general danger from radiation. This means few ever go that way but some might. Pirates looking to hide or PCs pursuing rumors of a lost/dead civilization. 

Space toward the north or top edge of the new frontier map is unexplored. 

As was said above the Great expanse borders the new frontier to the south or bottom of the map. Thus like the bad land it presents a border that few travel although in this case it's the few number of stars providing gravity wells to be the anchors for void jump technology (my own supposition on how void jump tech works). It's possible to jump to systems in the Great Expanse but you quickly run out of stars to jump to as they become more sparse. 

Incidentally Earth is approximately 1500 or more LY away in a north by north west direction and it's purely dumb luck that two different human colony expeditions ended up in this region of space to settle in the old Frontier and the new frontier. 

Rough conception of the location of Earth and the New Frontier approximately 4,000 LY between them 

My concept of the new Frontier as I described above

The Vast Expanse is a sort of barrier that cannot be transverse with current technology

The Badlands can be penetrated but they are considered dead and irradiated from the supernova that occured in a sector approximately 3 sectors to the west of the new frontier. The Badlands are effectively a barrier to expansion in that direction but could/can be explored 

To the east is the sathar and the original Frontier Sector ala Tom Stephans Expanded Frontier map. but not much exploration has happened in that direction. 

Potential ancient civilizations: the Clikks, the original planet where the heliopes evolved, Fore Runners which may actually be the Tetrarchs and the sathar are a huge "civilization" to the east. and were space faring at least a millenium ago (900 years ago they destroyed the Eorna Civilization) and probably clashed with the Clikks who abandoned the Heliopes on Starmist 700 years ago.