You can add a post-function to clone the current issue to another one with different issue type or a post-function to create new issue using the fields from the incident. You can put the post-function on a separate transition, so it will appear as a button in your "Incident" issue or put it on the create issue transition if you want this to happen automatically on Incident create.
If you check the Atlassian marketplace - there are a lot of add-ons that provide clone/create issue post-functions.
Can you provide some more details on why do you need that ?
Whilst not an answer to your specific question you may find these blogs interesting to read about how Atlassian consider Incident Management
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