Well, I`d like to see planet New London being depopulated and becoming uninhabitable world for the next decades as a result of this war. And it does not matter if Gallia wins this war or not.
How could this be achieved? Well I have two options in mind:
1. The GRN uses scorched earth tactic to demoralize their enemies (or instead unwillingly infuriate them). Besides trying to demoralize Bretonia / Liberty it could also be done due to their experience with planet Leeds. They do not have the ressources to start another long lasting ground battle while thei supply line in the Taus endangered (or cut off? not sure what it is ATM). So, they use all of their battleships for a planetwide orbital bombardement. Even if they loose this war, Gallia was here to punish their enemies and what would be better than destroy one of your most hated enemies`homeworld?
2. The nomads / Wilde perform a false flag terrorist attack during the ongoing battle, triggering some nuclear explosions on the ground and the atmosphere of NL, or some chemical and biological weapons here and there. It would not be a such a great attack like Toledo, rather a surgical strike with weapons used to weaken mankind further while Gallia will be blamed for it. Perhaps even the queen will be killed during the siege? Who knows. Gallia might even blame Liberty / Bretonia for making NL uninhabitable to deny them their prize. And back in a dark corner the nomads have a good laugh. (And to be honest I really prefer this situation rather than no. 1.)
Anyway, another result will be that system New Londong will be a huge wasteland with an depopulated planet, stations and lanes across the system either destroyed or barely in service.
Liberty will be forced to use even more ressources on keeping Bretonia afloat, literally being Bretonias new regents. Their fleets exhausted by the whole war makes them barely able to keep up the front, let alone set up a counter push against Gallia.
Bretonia due to the loss of New London is forced to set up a pawn government in exile either on planet Sprague or Gran Canaria (or perhaps Cambridge), with most of its economy and military being shattered. Aland will not be given up which results in more tensions with the IMG.
Gallia on the other side will leave New London system and keep a firm control over Leeds, Roussillon and Edinburgh when news reaches them that Ilse de France has fallen to Council. In the aftermath of this, the Gallia core worlds are being cut off one by one from the rest of Sirius, only a few home systems like Languedoc, effectively cutting off the Gallia invasion force from their homeworlds and reinforcements. What ressources they have will be used to set up permanent settlements on Gaya and Leeds. This also means what fleets they will have after the battle will be used as a defense against anything that Bretonia or Liberty will try to throw at them.
In the end all three parties come to a silent agreement that neither of them is able to continue this war although each of them will not officially propose any cease fire or peace talks because of all the hate that is flowing.
Well, those are my thoughts on the aftermath of the battle. Maybe I am wrong in some things because of certain actions that have happened in the past, but that I am not aware of as of now.