Hi @welder,
Jira does not allow you to filter issues by the status of linked issues, so no - not out of the box.
There's plenty of workarounds one could think of. If you are on the premium plan, you can filter initiatives with a certain status there and show the Epics underneath by showing the full issue hierarchy.
Or you could tweak the workflow of your Epics so you can make a distinction between new Epics and Approved Epics (or any other description that makes more sense). That way you could filter on Epic status. Automation would even let you transition your Epics automatically when your parent initiative moves to a next status.
In a similar fashion, you can implement any kind of tagging mechanism for the Epics through flagging, custom fields or labels you can update through automation as well, depending on the status change of those parent initiatives. As long as you can get the information you'd like to use for filtering on your Epics, you'll be able to achieve your goal.
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