Hello everyone, 

Priorities per project shipped with JIRA Server (including Core) version 7.6. At the time of release, this is not available for JIRA Service Desk projects. The release notes can be found here. This ticket will provide the visibility and progress on enabling this capability for JIRA Service Desk.
 
We would love to hear your feedback, so feel free to reach out to me or post a comment on this suggestion ticket.
 

Cheers,
Vidhu Sharma
Product Manager - Jira Service Desk