star trek - Why is there no Borg threat in the DS9 series?

Most of the contact the Federation has with the Borg happens before DS9. And Voyager has tons of Borg contact because it’s in the Borg-controlled quadrant of our galaxy, while Deep Space 9 resides far from active Borg space.

In late 2366, a Borg cube invaded Federation space and assimilated Jean-Luc Picard, whose tactical information contributed, along with the Borg's own vastly superior power, to Starfleet's disastrously one-sided engagement with the cube, the Battle of Wolf 359. A fleet of forty starships assembled to combat the cube. All but one of these ships were destroyed, while the cube remained intact, damaged but healing rapidly. The Enterprise-D recovered Picard and used his connection to the hive-mind to disable the cube before it could attack Earth. (TNG: "The Best of Both Worlds", "The Best of Both Worlds, Part II")

We witness some of this event in DS9: this battle is where Sisko's wife dies.

During the next few years the Borg face major set backs in the Delta quadrant; this is witnessed by the Voyager crew.

The next major incursion by the Borg into Federation space happens in 2373 (in the TNG movie First Contact) — the same year the Dominion War happens, a major plot theme in Deep Space 9. And as Richard states, this Borg attack is centered directly on earth, far from the Dominion War and Deep Space 9.