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 are able to join another clan. Also, if you are trying to rejoin a clan you were kicked out of, you'll have to wait 24h before you can approach the same clan again. The clan can however invite you back via the "Social tab", allowing you to join the clan immediately.
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.
Furthermore, a maximum of 10 pending join requests can be sent to each Clan at a time (requests initiated afterward will not fully process).
Just hang in there for a bit longer - you'll be able to join another clan before you know it.