It should not be a problem to do an import.
Export your data in the old environment to csv or JSON. (JSON works best)
In any screen in JIRA type "gg" a search box will open. In this search box you can type "External System Import" and select it.
Select the correct import format. Map the data to the correct fields and you can import it.
Here you can find some more info on importing JSON files https://confluence.atlassian.com/adminjiraserver071/importing-data-from-json-802592907.html
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