So the best answer depends on some details. But let's see if we can flesh things out here...
First you could consider configuring your board (assuming it is Classic and not NG) so that swimlanes are by Epic. This would illustrate all Epics that current have active issues on the board. What it would not show is say an Epic that doesn't have any issues on the board.
Next you could consider simply writing a JQL to retrieve a list of epics you are interested in. For example, if your board is based upon a filter like this - project = ABC, then you could perform an advanced search like this - Project = ABC and issuetype = epic and "epic status" != Done
Finally, you mention "delete the old ones". I'm not sure if you literally mean "delete" or maybe something else, like hide the done ones from the board. If you do mean delete I would strongly suggest you not do this. There is rarely an instance where you actually need to delete an issue or object in Jira.
If you have any questions PLMK.
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