I believe you're looking for the "Star Requiem" quartet by Adrian Cole.
Edited from the preface of the fourth book, "Labyrinth of Worlds":
Man once ruled over an Empire that stretched throughout countless worlds, worlds that formed a complex cycle, a self-contained chain.
In his hunger for knowledge, Man unlocked the door to another realm,
that of the alien race, the Csendook, and thus began a thousand year
war in which these ferocious aliens, faster and stronger than Man,
began the inexorable conquest of his Empire.
In desperation, facing extinction, Man's Imperator Elect and his
Consulate sought to escape the Csendook tide. On the world of Eannor,
the Imperator's Prime Consul and the principal scientist, Zellorian, used dark and forbidden powers to create a gate into a separate cycle
of worlds, a feat thought to be impossible. Zellorian brought the
Imperator Elect, his remaining Consulate and the last of Man's army
through to the world of Innasmorn, the Mother of Storms.
Innasmorn is a world of elemental forces, where the storms are worshipped as gods by its inhabitants. They, who are themselves
partly elemental, have no use for technology and have almost
completely outlawed the use of metals. When they learn of the arrival
of the intruders, the Men of the Imperator, they begin preparations
for war.
A small group of Innasmorians under Ussemitus, a woodsman, search for
a forbidden land far in the west of Innasmorn, which is said to
contain ancient powers. They fear that Zellorian will seek out these
powers and attempt to harness them in his new thirst for control.
[Elsewhere] Aurangzar, now Supreme Sanguinary of the Csendook, is
obsessed with the belief that the Imperator Elect is still alive. He
sends one of his loyal commanders, Vorenzar, on the trail of the
Imperator...
The part where a Csendook "hunting party" enters one of the portals:
Using an Opener, one of the Csendook sub-races bred for the creating of gates between worlds, Vorenzar finds a way through to Innasmorn.
At another point in the story, the Consul is sent through the gate:
Zellorian sends Pyramors back to Eannor in exchange for the safety of
his rebels. As he travels through the gate between world cycles,
Pyramors meets an Accrual, a parasitic being that feeds on the blood
and sacrifices that create gates. The Accrual promises Pyramors a
return to Innasmorn if he aquires sacrifces for it.
You can also read the opening chapters of the book here.
Note: There are similarities between this series and the author's own "Blood Red Angel" which was published later. Instead of an alien race, the ruling class in that book are highly-evolved humans called "Lightbenders". But they're cruel just the same. They use their portals to hunt and gather food, human species included.
