I recommend just blocking the person, if you're not on a blocking supported device, just simply ask your phone carrier to do it, or just change your phone number.
If it is intense such as death-threats, you can file a claim against it, typically against distress and disruptance of peace and such. However, if they don't go away after blocking them, it's always best to go to the police and see if they can assist with the threats.
The best plan of action would to contact a lawyer if the threats continue, as I feel the Police may not be able to do something about the offender if they are not in the police zoned area.