If you are going by "Only pureblooded Clanners can be soldiers in my new Star LEague" then the Wolves and Flacons are on one hell of a bind to get new troops. The Empire's sibkos aren't ready yet or getting absorbed by the Dragoons and the not Terra Falcons have other problems to deal with. That is probably the reason alaric demands that the other Clans follow him: a new supply of troops. Unless they start heavily recruiting former RAF personnel
except why would Alaric make that decision? the wolves made HEAVY use of freebirth warriors in the lead up to Terra.
The clans will likely follow a similer pattern on terra to what we saw in the wolf empire.
Academies on terra and in the "terran region" that the clans hold, will start churning out soldiers for the clans, efforts will also be made to recruit where possiable from the former ROTS.
republic factories in clan hands will swiftly be shifted to produce clan versions of the mechs produced (made easier as the ROTS is already doing this, expect to see clan tech Laments etc) and proably start producing clan mechs as well.
This BTW isn't going to immediatly happen it'll take a few years for Alaric to start seeing dividands, until then he's vunerable and is going to need to play it careful
now for some, TOTAL speculation.
so the genetic future of the wolves and falcons is in a bit of an odd situation with their sibkos quite likely out of reach and thus the collective genetic legacies of their past, quite possiably (very likely in the case of the falcons) lost to them, what do they do?
I'm going to take a guess that the long term solution is going to be to take a page from history.
The conquest of Terra is the msot important military action take by the clans since the Pentagon, Alaric could thus declare that very warrior who participated in the conquer of terra (wolf and falcon both) may start a new blood house. This would be excessive for the wolves (assuming the wolves have 30 clusters of 50 warriors left, that would be 1500 potential bloodname houses) but for the jade falcons would be very much a useful life line.
even if Alaric didn't declare this I imagine any freeborn warriors whom proved to be of "partiuclar worth" will have a very likely chance at a bloodname house.
doing this for the falcons could BTW result in both Jiyi's falcons and the terran falcons having a completely differant bloodname roster from each other, and one distinct from the falcons of old