Just a little FYI, security clearances have an end date. Two examples are secret and top secret. for a secret clearance, it lasts for 10 years. and for a top secret clearance, it lasts for 5 years. when it is about a year out from its expiration you need to go through the process of being investigated again to renew your clearance.
For high-level government individuals who come in without a clearance, they are given priority and can be given interim clearances that last for a year or so anyhow. I'm pretty sure that federal elected officials gain their clearance upon being elected, and it is very hard for them to lose it.
Also, just because you have a clearance does not mean you have access to information. All information is need-to-know. You need the clearance to be allowed access to sensitive information. So someone who leaves a job or even gets fired can find a job again where their clearance can be used, but they can't just demand information because they have a clearance, or have access to a secure location. The clearance allows for the permission to be given for the access, its not the permission for the access itself.
So people like Brennan can't do anything with their clearance other than using it to get a job that requires it anyhow. If a new administration came into power he could also get his clearance reinstated upon review.