The priorities are associated with Request Types. You can create a separate set of priorities for the new department and assign it to the Request Types they use.
Thanks Chris for the reply but i seem to either be misunderstand or something else is up.
The Tech Group has different Request Types however it doesnt allow me to say which Priority Types & Alerts to specify to the Request Type.
In Priority Types and Alerts i cant specify which Request Types are applied to each Priority Type
Priority is configured at request type/ticket level, doesn't matter which tech group/ tech is assigned.
You can select a default priority for a Request Type.
If a request type will be used by both departments, you can either
a) manually change the priority when a tech updates the ticket
b) configure the original request type to limit to department A with Priority A. Create another request type with same name (under same parent request type if needed), limit it to department B and use Priority B.