Brennan is no longer with the government. For what reason does he need a security clearance? What information is there that he has a “need to know”?
Brennan still has his clearance because, you know, patronage class and all. Qualifications and merit are assigned through consensus rather than any action on the part of the applicant. Look at Obama’s presidency. It’s the ultimate expression of the Patronage system.
Apparently it’s standard practice for some ex-intelligence folk to keep their clearances after moving to the private sector. At least that’s how it’s portrayed on Homeland.