When contacts are present on the account that the case is linked to, you have the option to add those contacts to the case.
Go through the Contacts tab on the case, click on the +Contact button, and choose any of the contacts showing under the Global Contacts section:
If the information on the contact needs to be updated, send the information to an admin who has access to your firm's accounts. When the contact information is updated at the account level, it will be reflected on all cases that have the contact.