The 7 day wait period from leaving a clan to joining a new one was removed on April 4th 2016. You can join and leave clans freely without any restrictions or cool down period between leaving one clan to join another.
That probation system was replaced by one that only allows you to skill in a Citadel once every week. So, if you had visited/capped Citadel in your previous/current clan, left that clan 3 days later to join a new clan, and attempted to skill in their Citadel, you would need to wait 4 more days to do so.