The Red Shard was a tactical response unit within the military guild charged with maintaining law enforcement and civil defense. Commanded by Kal-El (Superman), the Red Shard included his XO, Commander Asha Del-Nar, as well as several aspirants such as Sem-Re, Jeq-Vay and Kir Ta. Kal knew that he would have his hands full, particularly since many of the soldiers like Nar, could trace their military heritage back several generations. As it was though, Kal commanded their full respect and obedience -- save for Commander Gor, Zod's right-hand man, who perceived Kal-El's human compassion to be a weakness.
Kal's first mission with the Red Shard proved to be a civic defense matter. Zod informed him that a herd of wild Thought-Beasts were threatening to destroy some of the planet's atmospheric generator plants. Zod would have just as soon destroyed the beasts, but Kal-El used this crisis as a good training exercise for the aspirants. He trained them how to use their newfound powers to herd the Thought-Beasts away from the critical zones without resorting to wholesale slaughter. While Zod appreciated Kal-El's intuitiveness, he still believed his methods to be lacking in efficiency. 
The Red Shard's next crisis took place immediately thereafter. Disgruntled members of New Krypton's Labor Guild took control of the Council building, taking a number of hostages including Alura. In response, Commander Gor rounded up thirty unassociated members of the Labor Guild and threatened to execute them unless Alura and the other elders were released. Kal-El bargained with General Zod to give him thirty minutes to find a peaceful resolution to the matter. Zod reluctantly agreed, but sent sharpshooters to the crisis area ready to take out the Labor Guild leaders should Kal's plan fail. Superman succeeded in striking an accord with the disgruntled guild party and they laid down their arms. Commander Gor however, ignored Zod's order to stand down and tried to assassinate guild leader Tam-Or. Fortunately, Kal-El's cousin Supergirl was present and deflected Commander Gor's shot. This caused Gor to lose face within the military guild and he attacked Kal-El as a result. Having years of experience in the use of his powers, as well as being trained in hand-to-hand combat by the likes of Batman, Superman easily defeated Gor and the tension between them grew even worse.
In terms of law enforcement, the military guild also had to deal with their criminal element. Shortly following the release of Zod and the others from the Phantom Zone, the Zone itself collapsed, leaving several renegade Kryptonians free to do as they will. Thirteen known criminals were at large and General Zod gave instructions to several units on who they were and how to capture them. The most dangerous of the lot was a man named Val-Ty, aka, Greyline. Zod didn't feel that the Red Shard aspirants were disciplined enough to handle such a dangerous convict, so he left this task to one of his other units. As it was however, the Red Shard found themselves involved regardless. At this time, the Military Guild were providing several members of the Green Lantern Corps a tour of New Krypton when they came upon Greyline. Working together they quickly defeated him, but a dispute arose between matters of jurisdiction. Although Val-Ty was equally wanted by the Military Guild as well as the Guardians of the Universe, it was the Military Guild who maintained the right to prosecute him first. General Zod promised that after they were done with him, they would hand Val-Ty over to the Green Lanterns.