If you're on a 25+ user licence, then go to your my.atlassian.com account, find the Jira licence and look for the developer licence, that will give you a key for your new server so you can test everything before your actual move.
If on 10 users, then you can use evaluation licences. They will expire, but you should be small enough to get everything tested within the month + 2 extensions they will give you.
When you move, you can take the production licence across, it is in the database and hence export/import data.
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