How can the customer change the priority and type of a ticket?

When customers raise tickets, you would like to extend the ability for them to choose the priority and type of tickets so that you could plan the assignment and tracking of them. 

Please navigate to Admin > Workflows > Ticket fields > double click on these fields and verify if the priority field is displayed to the customer. If not, kindly choose the option 'Display to the customer' under customers end in ticket properties and the customer will then be able to edit it.