>>38406349"Permissions" in this sense is a practical arrangement between the owner of the IP and Cover ensuring that, within certain conditions, the owner will not pursue action such as reporting or issuing copyright claims against Cover's channels or videos that depict content related to the IP (such as gameplay footage from a livestream).
The reason it can often take time is that it needs to be submitted in a form that is legally binding at least to some degree. Copyright claims, even those made in error, can be seriously harmful to a channel and Cover needs actionable guarantees in order to protect its talents and its own revenue in the event of a dispute.
You might also want to mention that this policy is in response to Cover being burned before by IP holders mass-claiming livestreamed gameplay footage against them, or reneging on agreements that weren't legally binding at Cover's expense.