This can be accomplished through a data partition constraint. The data partition constraint would need to be associated to the data partition that is linked to the Role the users are using.
Table Name: Call_Req
Constraint Type: "Create"
Constraint: id = 0
This constraint will apply to the Call_Req table, which applies to Incidents, Problems, and Requests.
Using a type of "Create" assures that this will only apply for the creation of new cases, not existing cases (an "Update" constraint may be used if you wish to remove the ability to edit existing cases)
A constraint of "id=0" would only allow a person to create a new case if the id of that case were "0", since this isn't a valid id value they will be restricted from creating any case.