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You can use the existing license keys when you move the server from one machine to another (as long as there are no two servers running at the same time). As license keys are stored under <TeamCity Data Directory>, you transfer the license keys with all the other TeamCity settings data.
It is usually advisec advised not to combine TeamCity update with any other actions, like environment or hardware changes, and perform the changes one at a time so that, if something goes wrong, the cause can be easily tracked.
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