Alien options are a the bottom.
Let us suppose that we have a non-human sentient species that has
"evolved for war", i.e. has evolved significantly both biologically
and sociologically from a non-sentient state such that its members
consider a state of warfare as natural and right, and for there to be
an absence of war as quite unnatural and merely a precursor to a new
You'd pretty much have human beings. Prior to civilization and specialization of labor, all men were warrior and human-to-human violence was the major cause of male death.
As civilizations formed, warriors seemed to become a specialized caste but in reality that was just because it took a huge number of workers (tail or shaft) to support the military head (teeth or spearpoint.) The highest status individuals in all major cultures were warriors and warfare considered the most morally pure endeavor.
Consider the origins of the worlds, villain, vile and noble as they apply to morality. The first two come the latin 'vil' as in village and mean "farmer" the last comes from the latin for "famous name" and the 'nobel' of the West and the rest of the world were a caste of killers whose males trained from infancy for killing. Probably half the wars in history were fought for glory just because the "nobles" didn't have a purpose without war.
Now consider that the words for farmer mean evil and disgusting and the word for the killers means the most moral and you can see just how great a role war played in the past. All other major languages have similar evolutions.
The idea of world without war does not seem to ever popped up until less than 300 years ago in northern Europe. That's when war began to be seen as the anomaly instead of normal. What we think of as a normal moral attitude is a very, very recent cultural invention. Ethical universalism, seeing all human beings as morally equal who should be treated the same, is really less than 200 years old in the west, imperfect even here, and spreading only slowly across the world as advancing technology requires wider and wider degrees of cooperations.
Jerry Pournelle's once observed that, "Peace is an ideal whose existence we infer from the fact there are intervals between wars."
Likely, that is because prior to evolution of the corporation, large scale, long distance trade and technological progress, productivity changes only over the course of centuries. If anyone from individuals to people's wanted to improve their lot, their only option was to grab some of what somebody else had, land, food, minerals, population etc.
Heck, before capitalism, investing and stock ownership, the only way to get anything major built was by collecting taxes at sword point.
Given that all social mammals and insects fight collective combats that we could call wars, and that includes social apes, humans likely evolved from fighting primates. The same rules of evolution would apply on other worlds.
The only big difference we could imagine for a alien species would be physiological. Humans have no fangs or claws because of neoteny, the retaining of fetal characteristics. Likely, this is because our upright posture is the original posture of primate fetus. Neoteny probably helps with brain growth as well.
But other sentient species might follow another path. Humans can't have muzzles or fangs because we need our mouths to talk but it a species used their nostrils and sinuses to make sounds, then they could retain muzzles and fangs. Claws could be retained as long as they didn't retard grasping or helped it. Or they might take other forms. Could be anything as long it didn't get in the way of their becoming tool users able to organize on vast scales.
Since it's not necessary to evoke a particular impulse to war beyond what humans and other earth animals display, we don't need to assume that just because a species retained fangs and claws and whatnot that the mathematical logic of MAD would not work for them as well.
The real problem in making a space fairing conquering people is the economics. Once you've got enough energy to get into space, you've got enough energy to harvest all the material resources any planet could ever need.
To make a species compulsively warlike, they'd have to have a frozen technology and no productivity growth just like humans had in the pre-corporate era. They would have to have lost the idea that make a new resource and instead just keep trying to get more of the old just like pre-corporate humans never thought of making their own land grow more food but just of grabbing more land.
Precursor technology jumps them past the corporate/scientific/industrial era.
Before they develop the idea of progress, mass trade or resource creation they stumble across starships and weapons whose operation they do not understand. The advanced weapons might be AI with no will of their own so they just take orders from the first sentient that finds them. Our aliens just use the starships and weapons to extend their pattern of conquest to other worlds, never understanding they could harvest much greater riches at any random asteroid.
Note: The precursors could be their own ancestors who reached the stars then blew themselves up leaving only cave man survivors back on the home world to find bits and pieces of the old tech that still works.
Science forgotten, technology becomes ritual
In Jerry Jerry Pournelle's and Larry Nivens' Condominium series of the 1970s, the US and USSR become more worried about the spread of nuclear weapons and the destabilizing effects of advancing technology so they shut down most scientific research and contaminate scientific databases with bad data bring technological and scientific process to halt. Fortunately, this happened just after the invention of space travel.
Our aliens could do something similar but more extreme and off longer duration until they forgot science existed and their technology was produced and utilized by rote passed down as rituals through the generations. Again, with no progress and no ability to create new resources, they can only conquer.
Reavers take over
At some point, after the society becomes star faring, they decide to undergo a species wide genetic engineering program to make them incapable of aggression. But, some back-to-nature/primativist-cult that idealizes the old days of incessant war and hides out to avoid the transformation. When everyone else is rendered passive, they come out, and under the principle of "in the land of the blind, the one eyed man is king," take over and enslave the others, forcing them to create and maintain the technology they use to fight pointless wars of glory just because they think its what their species does.
Bored post-singularity hold-out, game players
Most of the population passes through the singularity and takes forms unidentifiable to pre-singularity beings. But some don't choose to do so but they've hit an advancement ceiling. What now? What do they have to do but loll around and play games. What happens to their society when natural competition for status breaks out into civil war. Much better to direct that bored frustration against other species.
Since they can't progress technologically and they might usually run into technologically inferior species, they make it a game, intentionally downgrading their technology to match their opponents to make it fair. Their entire culture would be based on seeking glory in war, regardless of how those wars are fought. Maybe they'd destroy or corrupt all the nuclear weapons on a world just to keep things going longer.
The aliens encountered are on a mission to wipe out any competing species before they become a threat to home world species. The warriors encountered are far, far from home and not equipped with the latest and greatest technology. They don't conquer but exterminate. Some thing like Fred Saberhagen's berserkers, but subculture of biological organisms instead of robots.