Sure, you could go with an Event or an Auto-Event that checks Conditions checks for the Contact and sets the Priority accordingly.
One good way may be to give these users with Special Handling conditions their own Service Contact.
Service Contracts - CA Service Management - 17.1 - CA Technologies Documentation
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A Service Contract also maps Service Types to common reference fields on a ticket, such as Priority and Asset. This mapping associates Service Types with attributes of a ticket. For example, an Organization’s contract can assign Service Types to each of the five Priority objects. When a ticket is created with a certain priority, the mapped Service Type is applied.
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Note - the customer does not need to have a physical Service Contract, nor even be aware of the CA ITSM Service Contract. It would be for your own management purposes, like many other fields.
(You can also go down the SPL route for unique one-off situations, but in general you should avoid this route when there are already out-of-the-box ways of doing things. See here to answer a different question with SPL code, as both an example of what can be done, and the complexity which might be the reason not to do it. SPL is a great resource, but it turns part of your system into "out of scope for Support" and introduces complexity.)
Thanks, Kyle_R.