All Time Tracking Data is stored within JIRA and should be migrated for you by Atlassian automatically. As for app/add-on it have to be reinstalled, and re-configured and all dashboard Gadgets or Email Subscriptions need to be recreated manually. See this Kb Cloud/Server Moving/Migration for more information. you could use Jira Cloud Migration Assistant to migrate from Server to Cloud. Refer to this KB https://support.atlassian.com/migration/docs/use-the-jira-cloud-migration-assistant-to-migrate/ for more information.
The license for Prime plugins for Jira Cloud will have to be purchased separately, you can see the pricing and the differences between them in this article https://bitbucket.org/tempo-io/servertimesheet/wiki/Timesheet_Reports_and_Gadgets_for_JIRA_Cloud .
But there is a benefit program: https://support.atlassian.com/migration/docs/cloud-migration-trials-for-server-and-data-center-customers/ that you can use on the migration!
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