Thank you for reaching out.
Unfortunately, it is not possible at this moment to hide done epics from the Epic Link drop-down in the child issues, however, we understand how this feature would be useful depending on how you are using JIRA.
That being said, we created a feature request to add this functionality to JIRA:
Feel free to vote and watch the suggestion to increase its priority and also receive notifications about any updates.
Let us know if you have any questions.
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