Back when Sandy Berger committed his unpunished crimes, I asked the same question about his clearance because he was obviously not part of the Bush administration. The answer was that his former boss, Bill Clinton, was the sponsor of his clearance.
Based on that, I'm going to say that Bathhouse Barry is the sponsor of Brennan and the rest of the former Obama officials who still have clearances.
And what is Obama's need to know? I say that in all honesty and it applies to Bush and Clinton too. The nation wasn't founded on the idea that Presidents have an entitlement to a lifetime of access to state secrets for their own purposes. They are in office and need that data, no question. But when they are out they go back to private pursuits and that need is over. If they choose to work for a thinktank then that's their right but they don't have a right to pull current intel data to advance that pursuit just because they feel entitled to it.