Not sure about cloud, but you can definitely do this on JIRA Service Desk Server. We do this exact scenario using the Bob Swift 'create on transition' plugin.
On the service desk workflow, you can create a post function on the 'create' transition (or any applicable transition).
Add the 'create on transition' post function.
Specify the JIRA project the new issue should be created in, copy over any fields to the new issue, and specify how it should be linked (i.e. relates to)
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