The army was established after the genocide of the Saiyans. Sometime before the events of Broly - The Legendary Super Saiyan, Broly had destroyed planets in the South Area while the army had enslaved the Shamoian race as their labor force.
Dragon Ball Z
Broly - The Legendary Super Saiyan
Paragus' Army came to Earth to lure Vegeta into a trap set for him on New Planet Vegeta, making him believe they want him to be their king. At that planet, the army had to face Gohan and Krillin who helped the Shamoians.