There is a support article titled How to import a project from a JIRA Server application to a JIRA Cloud application that may be of assistance.
At this time project imports are not available for JIRA Cloud applications as outlined on the Restricted functions in Atlassian Cloud apps. This KB outlines one of the workarounds to provide this functionality. Alternatively, if the history of the Issue is not required, you might consider the option to Importing Data from CSV as guided in
How to prepare a database export for a CSV Import from a JIRA Server application to a JIRA Cloud application. Finally, please vote on JRASERVER-40464 and JRASERVER-31806. Those two Suggestion tickets are being used to track the feature request to allow the import of Server projects directly into your Cloud instance.
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