There are some options for apps to add panels into the Jira issue view, but you are going to run into problems with duplication.
The panel you are looking at is a system generated panel, it is coded deep in the heart of Jira. When using the issue view, this panel grabs all the date/time type fields and groups them into itself, removing them from the general list of fields.
This is will not stop you from injecting another panel with whatever dates and times (or other fields) in it, but you will be duplicating what this panel shows, which is usually a bad idea for your users. Also, a simple injected panel will not allow edit of fields within it without a good extra chunk of coding, so where fields are editable, you'll need to go back to the main panel.
I want to ask what you're trying to achieve with a different panel, we may be able to help you do something else that meets the need, a lot more easily!
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