When your alliance has been taken over, Is it 24 hours you get it back?

You can't "take over" an alliance unless the leader has been inactive for about a week. At this point, any R3 or R4 member may spend 1000 diamonds to become the new leader of the alliance - and this is permanent.

This is done because it is a good assumption that a leader who has been away for a week is likely inactive. Alliances need active leaders more than anything to succeed. I suppose you can ask for the new leader to voluntarily give the alliance back to you - but they are not required to, and I am sure that your alliance would appreciate having someone active anyway.