The priority matrix can be used to set the ticket priority automatically based on the impact and urgency fields. You will have to navigate to Admin>Priority matrix and turn the toggle on. Once its turned on your tickets will get updated with priority automatically.

By default all incident tickets are raised with low priority and all service requests are raised with Medium priority. Please check if the priority matrix is enabled in admin -> priority matrix. Please reach out to our support team through support@freshservice.com for further assistance
Priority matrix would work only on Incidents and not for Service requests. This should be the reason why you are not able to see the priority change based on the Impact and Urgency of the ticket.