Public Security Department ( الأمن العام ) has started ab online portal to get permission to travel between one city to other city in case of emergency.
As it was mentioned before that for any permission to out during curfew hours you can on 911.
Here is the website link you can access to request online tanaqul.ecloud.sa/login
initially this website is launched in Arabic language. But Expats can use it by use any translator tool.
Now the have started an online portal where you can create account by using your ID card, Mobile number and personal details. Once you open an account for verification you will receive a message on your mobile to make sure that no one other taking this permission by using your information.
Once the registration is complete you can submit the request with complete detail of the emergency for you want to travel.
Public security department will process your request and after review your application, if they think your reason to travel valid. they will give you online approval.
This information is announced by official tweeter account of Public Security Department.