I'm afraid you can't. JIRA's priority list is global across all projects.
I am a big supporter of JIRA (I'm a JIRA admin), this particular limitation is high on my list.
For "software" projects, I want to have a specific priorities, such as "post-release enhancement" or "trivial",
but for "business" projects (same JIRA instance), I want to have very simple list (minor,major,critical).
I like the idea of JIRA Core, but I want to use 1 JIRA instance for Software and Business. This limitation makes it very challenging for me to do this.
Any plan in future to change this? For Issue Types, we can select 1 or more for 1 project (from a list).
Why can't we do something similar for Priority?
It's not possible to indicate that for particular Project or Issue Type by providing schemes for these also. I encourage you to try Extended Schemes for JIRA which allows you to set schemes and default values for particular Projects and particular Issue Types not only for Priorities but also for Resolutions and Issue Types.
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