There is no out of the box implementation available in jira to do this however a simple workaround can be that you create a copy of your workflow for issue type subtask and in the transitions leading to Closed status you define who would have the permission to do so.
You leave out this condition for the workflow which you apply to other issue types;
so that way anyone can go in and close any other issue type except sub-task.
Let me know if you want me to clarify my point.
Here's the link explaining you how to configure workflow schemes
I’m a designer on the Jira team. For a long time, I’ve fielded questions from other designers about how they should be using Jira Software with their design team. I’ve also heard feedback from other ...
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