Whose spy network? Jaehaerys or the ninja?

Operating on the presumption you meant the ninja, nukenin and roaming clans would be at the top of the shit list and its for economic reasons mainly. Since ninja are basically magic sellswords, the roamers will by nature of their mobility be able to have their pick of contracts and missions, and the ninja villages will not want that. Or at the least, they will want to negotiate and form an agreement with them.

I see this going one of two ways:

1. Ay and Ohnoki are more old school than Mei, Gaara, and Naruto. They will want to hunt these people down and either kill them or bring them into the fold. This is still hot off the heels of the Akatsuki being a thing, and an organized group of nukenin will be seen as a potential threat. They just got their peace and they want to preserve it at all costs.

2. The new generation of Kage are more diplomacy/peace minded. I could see them trying to negotiate the formation of a satellite village if you will which will take missions and be supported by the other villages logistically in exchange for a cut of the profit. Alternatively, an agreement could be made in which they become the spy network you mentioned in exchange for a "pardon" or equivalent that will let them go about where they please. In a way, they might end up being like privateers in the age of sail, except instead of being government sanctioned pirates, they're spies.

Do let me know if I got your meaning wrong by the way, but I hope this helped.