The general idea is that after Jakku, what was left of the Imperial military either surrendered, or fractured into many different factions and warlords, referred to collectively as "Imperial remnants". Basically anyone above the rank of Captain, all of the surviving Moffs (and one assumes *everyone* from ISB) that didn't defect or surrender are automatically declared wanted war criminals, with bounties and warrants out for their capture.
Most of these factions are small-time, tin pot wannabe dictators operating on the fringes. None of them being a particular threat on their own, and collectively too much hassle to go digging them out until they actively make a nuisance of themselves. Most seemingly have little more than a few medium sized frigates, corvettes & support ships, plus an ever dwindling supply of TIEs. If any of them have anything anywhere near as formidable as a destroyer, then they probably make damn sure they keep it out of sight of the New Republic, and that's even assuming they have the parts and personnel to keep the thing running. The last thing any of them wants is the full attention of the NRDF.
On the civilian side of things; what was left of the centralised government and bureaucracy (represented by Grand Vizier Mas Amedda, who was basically a puppet anyway) formally surrendered to the New Republic and signed the Galactic Concordance after the final battle of Jakku. That's where things like the rehabilitation programs, disarmament, and hardware reclamation projects come in. A small fraction of worlds remained stubbornly (and after Cinder; bafflingly) loyal to Imperial rule and end up becoming rogue states, which are easily isolated, and pose little threat without the Imperial fleet to back them up.
How the First Order fits into all of this is that they're what eventually became one of those military factions that split away from the rest. Specifically the ones selected by Palpatine to survive Operation Cinder; the true hardliner fanatics, bordering on cultists. They all took off into the Unknown Regions with a fair amount of hardware at Jakku, leaving the rest behind to burn. Their main purpose seems to simply be a stateless military, there to mostly be used by Palpatine's clone as a pawn to neutralise and suppress the New Republic after the Starkiller decapitates it.
That's all still a generation down the line though. Right now it's about five-ish years after the formal surrender and there's still some remnants knocking about. Some laying very low, jealously hording their merger resources and territories, others operating as little more than pirates and raiders in outland regions and wild space. Most of the major ones (including the First Order To Be) are on the "Shadow Council" which ostensibly tries to coordinate between the factions while maintaining the outward appearance of a disorganised rabble, but really seems to spend as much time and energy on actual in-fighting as anything else.
That's the real threat Thrawn represents; he could finally unite the bickering renmants and turn them back into an effective force with sane leadership and start seriously undermining the New Republic. Of course he likely doesn't know Palpatine's insane clone is pulling some of these strings, and won't take too kindly to someone co-opting his plans, but I wouldn't be shocked if Thrawn recognises his hand in some of what's going on. How that would play out is rather interesting in and of itself.
