The release of CAS numbers is a continual process, so there is no exact date you should expect to receive your CAS. All relevant communications from Admissions will be sent via King's Apply.
If you have an unconditional offer, then your CAS number will be issued once you have paid your deposit. Admissions will then invite you to visit a new "Your Visa" tab within King's Apply. This will contain information for you to confirm and once this is done, you should normally receive your CAS number within a few weeks.
If you have a conditional offer, then you will need to send your exam and/or English Language results via King's Apply. If you are sending a digital transcript, such as HEAR, then these documents need to be sent securely to email@example.com. If Admissions require any additional information from you then they will contact you via King's Apply.