As others have said, the Union is going to be in this for the long haul. Necromunda is probably one of the most messed up worlds in the Imperium of Man that still has a significant human population on it. But the Union does have a couple technologies that would help them accomplish the process of bringing a level of sanity back to Necromunda. I'm going to assume that Necromunda was basically dropped in a system with one of the blink gates, otherwise the Union wouldn't be able to reach it before everyone there starved to death.
First are the printers. Printers in Lancer are a lot like today's 3D printers on a big pile of steroids. If it has raw matter and the schematics of what you want, it'll pop out copies of it pretty much instantly. It doesn't do as well with biochemistry though, but it is capable of printing emergency food called 'printloaf'. One can live off of printloaf, but it's pretty bland and unappetizing. Which means to the people of Necromunda (outside of the nobility), it's as good as a 5 star meal.
Second are the NHPs. While Union does have sub-sapient AIs called COMP/CONs, NHPs are different. They're essentially eldritch bodiless entities encased within a system called a Casket, which enables them to exist in our reality and think much like a human does. They're capable of very impressive feats of calculation and analysis, and their processing speed is virtually infinite, limited only by how fast they can get data. For example, there's a group of five of these somewhere in the Union that form an extremely accurate predictive model of the known galaxy. Warships of the Union all have one for a central computer, and some warships are crewed almost entirely by the NHP and supplementary Comp/Cons and hardly have any human presence at all.
Third is hacking. Even base lancer mechs can hack other mechs and cause trouble in their systems. Mechs with NHPs can do some really alien stuff like bending time or dragging enemies into blink space. Capital ship NHPs that are in combat can attack with paracausal viruses sent through blinkspace in a war that is just as vicious as the bombardments in reality. The information security of Necromunda and the machine spirits won't stand a chance. The moment the Union lands, they will own the local networks. Any camera or microphone becomes eyes and ears for them. More importantly, the Union can use this to learn of the dangers waiting for them on the planet, once they get into Inquisitorial systems. They'll be forewarned about the gangs, the adeptus mechanicus, which nobles will likely be difficult, and the possibility of gene stealer cults and chaos cults.
So, the Union arrives, and they see just what a hellhole Necromunda is. And they quickly realize the mass famine that will soon break out without regular Imperium shipments of food to feed the massive population. A whole lot of industrial grade printers are going to be shipped in ASAP, and landed on various places of the world. These will need both protection from the constant acid rains, and from the numerous gangs, cults, and other factions that inhabit the world. The Union certainly has the technology to do the former, the printers can make it themselves in fact. As for the latter, a team of lancers to guard a printer would do it. Few would be crazy enough to pick a fight with the big stompy mechs.
Anyway, I see the Union setting up several bases over the world, outside of the hive cities themselves. Any wide open spot of barren wilderness will do, as the Union will need lots of room to expand each of these bases. The printers get set up, and immediately put to work. The Union likely has schematics for small emergency self sufficient shelters, ones that can be stacked up like apartments, that have power, plumbing, and other necessities built into them. Several printers would be focused on churning these out as fast as they can. Others would run pumps and pipes to the literal oceans of fecal matter that accumulated over millenniums from the hive cities dumping their sewage in the wastelands. These printers would use this virtually infinite supply of biomatter to mass produce printloaf to head off the coming famine.
From each of these bases, the Union starts the looooooong process of cleaning up the hive cities. The NHPs could easily hack into whatever communication or public address systems of Necromunda, and start broadcasting their offer of aid. 'Come to the Union. We've got food, shelter, clean water, medicines, and the like.' The nobility probably won't like this, but the Union can be diplomatic. Nobles can be offered a chance to assist and be on the right side of history, and in return be allowed to retire in luxury and comfort. Otherwise, they're soon bound to be facing a riot of starving people, or the big stompy lancer mechs themselves. Gangs and such would also receive an offer, a chance for clemency and a fresh start, a chance to rejoin civilization with a clean slate and not having to live in the underhive. I could see the Union even winning over the local Adeptus Mechanicus, if they dress up their stuff as STCs, and conceal the NHP's true natures. Or present them as a sort of super machine spirit.
Anyway, the Union bases are going to have a flood of people coming their way. Steady food while starving has a way of overcoming xenophobia and fanaticism. The printers are going to be hard pressed to keep up with demand. Things will be crowded for a while, with the printers running 24/7 to make the needed shelter and food for the coming people. But the Union is very efficient, and with an NHP coordinating logistics for all these bases and growing refugee cities, they can ensure there's no wasted time or resources, and the needed material and food gets to where it needs to go. The Union begins a process of medical screening, treating diseases and correcting mutations, even cloning replacements for missing limbs and organs. These screenings will also identify genestealer infections, and with the Union medical knowhow, they could be cured I imagine. The refugees will also likely need to be educated and taught the basics of using Union technology. It will take a while, but eventually they'll be able to assist the Union personnel with the massive humanitarian effort.
Naturally, not everyone is going to accept the Unions offers. There'll be nobles who cling to their power, gangs who answer to no one but themselves, cultists who are too fanatic to be tempted by food and shelter and safety, crazed mutants, suspicious or xenophobic people who simply think the Union's offer is too good to be true, and the like. There may be some that openly attack the growing refugee cities, but those would be put down by the lancer teams. NHPs owning the local information networks would keep any resisting groups from being able to form a unified front. If a stubborn noble transmits an order for his guardsmen to attack, it'll get intercepted mid transit by a watching NHP and changed into an order to surrender. Any stubborn holdouts can be isolated with control of the hive city's systems thanks to the NHP hacking. Once a few nobles are taken down, the rest likely would accept the Union's offer. For gangs, mutants, and cultists and such, armed drones could be mass produced, or lancer teams sent into the deeper parts of the city. The goal will likely to be to stun, apprehend the holdouts, and bring them back for rehabilitation and/or curing of mutations. The drones will likely also be needed to search the parts of the city where communication simply isn't possible, such as the deeper levels, and letting survivors there know that help has come.
As the hive cities gradually empty, and the flood of refugees slow, the printers can be turned to making the refugee cities into proper ones, with the different facilities that a city would need. The NHPs would ensure proper planning is done to prevent any wastage from happening. No multitude of mutant and toxic waste filled underlevels of the old hive cities. The old hive cities would likely be dismantled for raw material to be fed into the printers, though any items of cultural, artistic, or religious significance would be preserved and brought back intact. With basic survival needs met, more attention could be given to improving the quality of life. Hydroponics, vertical farms, and meat cloning vats are set up, to provide better food aside from printloaf. Actual homes are built, letting people upgrade from the basic cubicle with a bed, bathroom, and kitchenette. Actual schools and universities are built to give the coming generations a proper education. More attention is given to cultural and artistic endeavors, even entertainment ones. Religious ones as well, as I imagine the people would insist on building a few cathedrals to the God Emperor. And eventually, terraforming equipment gets printed, to start reversing the horrible damage done to the ruined environment.
It will be the work of decades and take a lot of resources from the Union to pull off. But in time, and thanks to the Union tech and NHPs, Necromunda would eventually be transformed from a toxic brutal hellhole into a vibrant garden world with pristine cities. People born in abject poverty would live to see their children and children's children live in prosperity. And in return, the Union researchers and NHPs get their hands on warp drive tech. They could probably modify it to work with blink space instead, and give the Union a proper FTL engine.
Mind, I don't think the Union could pull this sort of recovery off with more than one hive world at a time. It would tie up a big chunk of their fleet and resources, after all. But the Union is humanitarian enough to embark on a huge restoration project like this.
