No, the user would have to be a JSM Agent to be able to update any field, including the Priority. Customers can add comments and maybe even Approve a transition, but that's pretty much it.
You must be a registered user to add a comment. If you've already registered, sign in. Otherwise, register and sign in.
Based on my searching, it is not possible for a customer to change the priority on a Service Management issue after it has been created, with native Jira functionality.
You might be able to find a third party app that would add that functionality to your instance. I found one mentioned in another post, but it is only for Server and Data Center, and not available for Jira Cloud.
You must be a registered user to add a comment. If you've already registered, sign in. Otherwise, register and sign in.