So, a bit of a look at mid to long term threats for us right now.
Well, in my opinion our response to both the Orks and Chaos should be basically the same. Expansion.
None of the local Ork or Chaos domains are a serious threat to the Trusts survival. While a campaign started by them might hurt us, they don't have what it takes to overwhelm our superior naval and armed forces. Any single Chaos domain is vastly inferior in numbers and quality to either the Trust or the Blood Dragons, never mind both of them allied. And while we know that a Tier 2 Waagh can hurt us and might have a shot at overwhelming Dragons Nest, Waaagh Gutcrumpa was apparently about as powerful as a Tier 2 Waaagh gets due to being almost entirely made from combat veterans and elites combined with a superhulk. It is safe to assume that any Waaagh Tugozaks domain spits out will be significantly weaker than Gutcrumpas. The only other possibly serious local threat is the Tzeentchian domains rumoured superweapon, but we know almost nothing about that.
We should still spare some attention to our neighbors though, since a local annoyance can possibly spiral into an existential threat if they manage to eat each other and combine. For example, the Tzeentchian and Slaaneshi domains might actually be a challenging enemy if they set their differences aside, and if a Waaagh spawned by Tugozaks domain eats one of the Chaos domains or a significant part of Dragons Nest they could conceivably grow to Tier 3 and become all but impossible to defeat.
Other than that, the Necron dynasty in our neighborhood might be an existantial threat if we piss them off, but they are currently distracted with other stuff. We would need to provoke them to draw serious attacks from them. Still, it is entirely possible that sometime in the next century the Necrons finish off the Tyranid onslaught and return their focus to local matters, so their presence should not be forgotten.
The main threats to us come from farther afield. Both Chaos and the Orks could trivially send forces capable of crushing our little corner of space. A Tier 3 Waaagh or a serious Chaos Crusade is easily capable of finishing us off. There is really very little we can actively do about the former except hope and pray the Beast doesn't come our way. Chaos attention can potentially be avoided by making sure we don't have any Chaos domain near us to call in support from elsewhere, but all in all that is a bit of a crapshoot and might even backfire with Chaos' divination capabilities.
Our strategic directive is therefore easy: Grow enough to be able to fend of a random Tier 3 Waaagh or a serious Chaos Crusade. Technological improvements or investments in our armies quality are not enough to do so.
We need more ships, more troops, more industry, more planets. More everything, really, to survive the attention of the Black Imperium or an Orkish Waaagh fattened on a sector rolling into our neighborhood. To do so, we need to fuse with the Dragons Nest so we can comfortably equip them with the entirety of the Trusts technological arsenal. Then we need to eat all of our neighbors and repurpose their planets to churn out armies and navies for us. Tugozaks domain is a security risk as long as any other Domain is around they could conquer to turn into a Tier 3 Waaagh, so it has to go as soon as possible. The Chaos Domains should be easy pickings, so take them and purify their planets so we can make use of them as soon as possible.
Expand or die.