Are you talking about ServiceDesk or your own workflow?
The idea is simple, use send e-mail component (or SD.EmailServices) based on priority value. Where to do this, depends on the exact goal.
If the email sending needs to happen somewhere where there's chance of sending the mail erroneously or the workflow loops (e.g. Initial Diagnosis in SD.IncidentManagement), you can use an added variable (like NeedToSendUrgentEmail) that's set when the priority is changed and unset after email is sent.