I think banned account cannot be recovered. so, you have to register for new account.
It isn't the account that gets banned, it's you (as a person). If you are permabanned, and register a new account, it's called "ban evasion", which is a bannable offence if you get caught.
You are allowed to create a new account and open 1 thread (only 1) in the meta subforum to discuss your ban. That's all... If you PM, open a second thread, create a thirth account, you're evading your ban and risk your other account(s) to be banned as well.
If you are permabanned and you don't know why, create this new account, open 1 new thread in meta and ask why you were banned... After you get your explanation, log out and stay away from the forum for a couple of months.... When several months have passed, you can (potentially) appeal using the one (and only) allowed thread in meta you opened earlyer and hope the admin is in a really good mood and gives you a second chance (altough i wouldn't get my hopes up)