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I have created an additional hierarchy called a Theme above my Epic. When I update the parent link in the epic, it is not updating the plan. The new child does not appear.
Sounds like you have the custom field, Parent Link, added to your issue types, per https://confluence.atlassian.com/advancedroadmapscloud/showing-portfolio-custom-fields-in-jira-998651396.html
Does your plan source filter/board also include the Theme and the Epic?