The exact relationship was never defined in explicit terms, though the freelance nature of the schoolteachers, Pyg involvement and connections to Scorpiana and others at least indicate that St. Hadrian's had a working relationship with Spyral and was an asset that Dedalus might have been able to bend to Talia's purposes with the Leviathan campaign. We also knew that Hood was working for T.H.E.Y. (as was the traitorous first Matron) so essentially, once Dedalus's escape and subsequent theft and sale of Spyral assets to Leviathan happened, Kathy, connected very much with T.H.E.Y., and St. Hadrian's itself is Kathy's brainchild, swoops in and cleans up the whole situation, taking over the remaining assets of Spyral and becoming the new Agent Zero to clean up her father's mess. Everything about St. Hadrian's reflects Kathy. The skull girls wear original vintage Batwoman costumes with skulls. They use the original Batwoman purse style weapons. The Son of Pyg reflects the Daughter of Dedalus, while also ironically I guess paralleling the pig/spider relationship of Charlotte's Web. Scorpiana, prize pupil of that school who has become an evil assassin and affiliated with the Black Glove's Club of Villains, keeps turning up, and has some incredible parallels with Kathy's relationship with El Gaucho.
Spyral was effectively defunct when Dedalus escaped his island and started reactivating secret stashes of assets, and Kathy was presumably running St. Hadrian's and T.H.E.Y., so the Spyral takeover was something that was then re-taken-over.
Retro315 no more. Anonymity is so 2005.
retrowarbird.blogspot.com
Maybe i missed something by I still don't really get why Spyral is evil (or more evil than other spy agencies) and has to be destroyed.