RealGM

Say a team is $8 million under the cap (salary wise), but has the MLE, the BAE, and TPE's totaling $9 million. They renounce those exceptions and then sign an unrestricted FA for $8 million.

Do they then get those exceptions (MLE, BAE, TPE's) back immediately or is there a certain time they must wait to get them back?

Any exception that is renounced is gone, they don't get it back. The following season they would get the MLE again on July 1st and also the BAE, since they obviously didn't use the BAE if they renounced it. Any renounced trade exceptions would be gone forever....