That’s a cool idea. Honestly you could’ve had something similar to what was already in the films. The First Order could’ve been your Imperial Remnant, fighting with the New Republic, then a Sith Cult out in the Unknown Regions introduces a new threat that brings the two factions together. Maybe they wanted to resurrect a Sith Lord and begin a new Sith Empire. Could’ve been Sidious, or Darth Bane, or a brand new guy.
I’d have made the First Order Luke’s Jedi Order after Kylo Ren fell to the dark side and booted Luke and his loyalists out — a dark side cult/terrorist faction hostile to both the New Republic and Imperial Remnant. They would’ve manipulated events to get the Republicans and Imperials embroiled in a new war, would would’ve destabilized both sides, leaving them vulnerable to the First Order’s true masters — alien invaders from the Unknown Regions.