Star Wars: Birth of the Republic
The Azure Imperium
Like Coruscant and Alsakan, the Azure Imperium didn’t suffer much under the reign of the Infinite Empire. Unlike Coruscant, however, the Infinite Empire never got the chance to try and use them as a staging point. As the free worlds moved north, spearheaded by Corellia and the Duro Kingdom, forces were moved out of the Empire’s vassal worlds along what would eventually be the Perlemian Trade Route, leading to the Battle of Coruscant, which ended in a decisive victory for the free worlds when Coruscant defected to their side early on. And neither Axum nor Anaxes were involved in the slightest. Axum quietly threw their own coup against remnant Imperial forces in their system, annexed Anaxes after finishing off the Imperial garrison there, and then began a military build-up, expecting the Infinite Empire to return any day. And then some Duros traders popped in and asked if they’d like to buy a hyperdrive, and the Azure Imperium realized that it wouldn’t be a thousand years before the dream of quick and efficient travel between the stars would be realized.
The end result of this is that the Azure Imperium is self-sufficient, industrialized, militarized, and fairly suspicious of the other political factions. They were never really part of the decade-long bonding exercise that was the Revolution, and though many (especially Corellia) insist that the Infinite Empire has not yet breathed its last in the Core Worlds, the Azure Imperium is turning towards what to do now the Empire is gone. The most pressing question for the Azure Imperium has been what would happen should the other worlds decide to annex them. And their answer has been fairly militant. Though they are not willing to declare open war (at least, not yet), they have made no secret of their desire to annex the neutral worlds along the Perlemian Trade Route in order to secure their flank, nor of their suspicions that Alsakan may attempt to annex them by force. This has led to an arms race between the Imperium and Alsakan, pushing the two of them to the brink of war, both mostly waiting for one side to fire the first shot.
The situation with Corellia is little better. Though the Azure Imperium and Corellia aren’t adjacent to one another along any hyperspace lanes and thus getting to each other would basically necessitate cutting through systems controlled by Coruscant and their allies, the two nevertheless have an intense dislike of one another. Corellia sees the Azure Imperium’s refusal to join in the hunt for the remnants of the Infinite Empire and their desire to annex other worlds as both cowardly and tyrannical, and little better than the Infinite Empire itself. The Azure Imperium, for their part, would be more than happy to attack Corellia and Kuat after they finish up with Alsakan and Coruscant (regardless of the plausibility of their winning such a war).
Being quite distant from them, the Azure Imperium has no immediate concerns with the Duro Kingdom, and likewise the Duro Kingdom is interested in keeping good relations with the Imperium in order to keep the trade routes north open.