After leaving a clan, it may take some time for the system to recognize that you've left. This may result in a delay before you're able to join another clan. Also, please note you won't be able to join a clan if you have been previously kicked out from it. If this is the case, you will need to be invited to join the clan to be able to be part of it again.
If you're trying to join an "invite only" clan, please remember that you can only send one invite request to a clan at a time. You will not be able to send another request if you're still in a clan, or if your previous request still appears in the chat window of the clan it was sent to, even if this request has been rejected. You can join a clan immediately if you get a direct invitation from the clan leader/ clan elder.
Just hang in there for a bit longer - you'll be able to join another clan before you know it.