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Today, Jira automation only have actions to edit/modify Jira features (issues, releases, etc), so there are no actions to edit other application features (As bitbucket, Github, etc).
That being said, I'm afraid the only way to achieve what you need would be to create your own script integrating both applications, using a REST API call to properly create the pull request based on a Jira Webhook.
You can refer to the documentation below for more details:
I hope this information helps.
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