‘The Day Of The Doctor’ could be an example of the first successful alliance with an alien race, thanks to the Doctor engineering it so both parties were concerned with making the best deal for all involved (because they didn’t know what side they were on).
The Doctor seems pretty convinced that this will work (and it is presented as being the conclusion of that particular plot thread), at least in the short term. This should be incorporated into any adventure set after this point so we should think about what form this alliance takes place.
The Zygons’ main priority is obtaining a new home but also a degree of comfort. Their placement in stasis was quite a gamble, as they had no way to anticipate how Earth technology would develop. It might have never achieved the level of advancement they needed or it might have become too powerful to overcome. They were lucky that they gained access to a stockpile of alien artefacts.
The concern voiced during the treaty is that the humans could destroy the Zygons, just as they did with the Sycorax in ‘The Christmas Invasion.’ For once it is the humans that aren’t perceived as trustworthy.
The British (and by extension the rest of humanity) would be concerned with whether they could support the introduction of the Zygon population. There does not seem to be too many Zygons within the paintings (since they are all empty and were able to hide by destroying a few statues) but there could be others in stasis elsewhere or aboard a refugee fleet (although how would they know when to arrive?).
They’d of course worry about an attack from a warlike species, especially as this contact was initiated through an invasion. Luckily the Zygons practice of keeping their human doubles alive will reduce the possible casualties already inflicted.
The key to this was the Zygons desire for comfort. If they have no desire for conflict (due to their experiences in the Time War) then it only matters that Earth provides an environment suitable to their needs. Their decision to emerge in the 21st century suggests that it is and they don’t need to alter it further (as they have attempted in the past).
The Zygons’ ability to shape shift would help maintain secrecy, as they could mix with humanity without being noticed. They already display the ability to assume the form of another without a captive. It is possible that they can assume a human form long enough when out in public, returning to their natural form when in private.
Alternatively they could assume the forms of those in comas or who are on life support (their biotechnology might actually help the patient). People could volunteer to ‘rent’ their form for a limited time.
Possibly a Zygon could learn to create their own original human form. This would remove the need to have a template to copy. Surely the Doctor could show them a thing or two about taking a convincing human shape.
From what we hear of the treaty (under Clara’s conversation with the War Doctor) it appears that the Zygons will share their biotechnology with the humans. Thus the humans can’t get rid of the Zygons without loosing the secrets of their science.
This could lead to a new wave of biological technology, used firstly by UNIT but which might eventually be used in the public sector. This creates exciting possibilities for the near future.
Adventures set in the mid to late 21st century might feature biological implants of all types (bio-punk rather than cyber-punk), computers with organic intelligence and living vessels (taking us a step closer to a TARDIS). Not to mention advances in genetics that could resurrect extinct species.
Whatever form the treaty takes it has to be so good that when both sides remember whether they are Zygon or human they still abide by it. If we assume that it is peace would be a fragile thing. There would need to be safeguards in place to ensure it is upheld.
The first step would be finding a place for the Zygons’ to live. With the current housing crisis this could be tricky, complicated further by a need to prevent people finding out the truth about them.
Due to their amphibious nature the Zygons could find homes in sections of water perhaps within their organic spaceships. The question would be whether they would find this comfortable enough.
There would need to be an agency policing affairs between Zygons and humans, ideally with agents from both sides. If Zygon is injured or murdered this agency could be assigned to investigate, to establish if it is was a violent attack and to punish the guilty.
This could be the basis for a buddy cop adventure or campaign. The victim could have been killed just for being an alien, they could have been killed by another Zygon (maybe hoping to stir up discontent between the races), killed by someone who didn’t know they were alien (maybe it was a robbery that went wrong) or it could be an accident.
The same agency might also be responsible for ensuring that the integration is working, checking up on those Zygons who have been placed in human society. Not only must they make sure they are maintaining their cover but they’d have to deal with tricky situations like what happens if a Zygon falls in love with a human who doesn’t know they’re an alien.
If the treaty did begin to breakdown both sides might resort to the same methods to restore peace, wiping the memories of those negotiating. Memory wipes could also be used to fully integrate a Zygon into a new human persona.
Adventures could be based around the development of new biotechnology. Can the humans use it responsibly? Would they become impatient with the rate in which were releasing the knowledge? Might the humans decide that they no longer needed the Zygons to advance their biotechnology, threatening a linchpin of the treaty?
As long as the peace treaty remains in the place the Zygons become a new potential race for the players to choose. A TARDIS crew with a friendly shape shifter onboard could be a real advantage, able to infiltrate the enemy or impersonate historical figures to ensure that history goes according to plan.
A UNIT campaign might introduce Zygon soldiers. They’d have their own natural weaponry and their shape shifting would be a real advantage for espionage. Zygons could also find themselves ideally suited for protecting targets, even assuming their form to act as a decoy.
It is up to you how long this peace does last. It might last forever or it might break down at some point resulting in a conflict (which you can centre an adventure around). Of course the Zygons might eventually find another world to settle on and call home once more.