Strictly speaking, you should buy a second licence, as you will briefly have effectively two production servers.
However, do not do that. Your migration is a perfectly normal thing to do, and Atlassian cater for it directly. Commercial licence holders have access to a "developer licence", which is intended for development, testing, keeping cold standby machines ready, and assisting with migrations and upgrades.
You also have the option of using evaluation licences, or, if you're particularly lazy, just cloning the old licence. Whilst those are technically naughty, Atlassian tend to go with the spirit of the licence over the legal minima. Your intention is to migrate from one server to another. If you end up with one new production server, they're not going to have a go at you for hacking around with slightly inappropriate licences for a few weeks while you prep and test the move.
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