Maybe you are not sure that if you have 7 days to use it, or if there's a 7 day cooldown on when you can use another. So the 7 days is the duration of the item(cheap aika gold) in your inventory, or something like that?
The designation on the Exile Warrant means that the item itself expires in 7 days if not used, not that nationality changes only last 7 days. Exile Warrants can be used as often as you like, provided they haven't expired and provided that the one you're using was bought while you were in the nation whose citizenship you want to give up.
Your nation will be wiped and you can redo your citizenship quest in the nation of your choice. So we bought the item in Lenaria, used it and had no nation. Then went to Feonir to do the citizenship quest (if your level higher than 15 you only can do it in the PvE channel) and then after completing the quest we were from Feonir.
This item causes you to no longer have a nation in Aika. You will have to pay the fee to join another nation if you wish to have one, but can choose any nation you desire.