From what the H.I.V.E. has done in the past it should at the very least be after Brother Blood has been taken into custody. From the start the Academy had more of a high school kind of feel and produced supers for hire. They graduated and did jobs. It was the ones in charge that directed them more toward villainy. Presumably someone like Jynx would take charge and let the students decide for themselves. 

I personally prefer original characters over son/daugher of so and so. I think if H.I.V.E was only a few (2-3) years after Blood going away we could pick up during a reconstruction phase. It would be more dynamic because they would be trying to debunk a stigma as opposed to being "just another institution." And the ones in charge would also be learning along with the students. Then perhaps we could introduce more seasoned supers to fill in the experience gap.