Let's gather some more background information to understand the true requirement.
You did not indicate what kind of tickets these are (Incidents, Problems, Requests, Change Orders?)
You do know that Service Types (SLAs) can be associated to categories, organizations, configuration items, contacts. Why is this requirement tied to a new (undefined) priority? Priority is primarily a factor for Incident Management that relates how important an Incident is, relative to other open incidents, to the organization as a whole. Priority helps to direct organizational resources.