Annoying as it sounds it is very unlikely any new TLD such as .ICP will be allowed by ICANN as a one-off. It will have to be applied for (along with many other hundreds and possibly thousands of applications) in the second round of new TLDs. Applications for the first round of new TLDs (like .APP and .BIKE etc) were opened early 2012 and the first approved new TLD went live for general use in Feb 2014, 2 years after applying. Applications for the second round won’t go ahead until ICANN has given the go ahead to the process, which it hasn’t yet. According to reports the ICANN board will not approve the second round until Q2 2022 at the earliest. With improvements to the application process and assuming Dfinity gets the string (they will be competing against other applicants) it is unlikely .ICP will be available for actual use until Q3/Q4 2023. Even then this is a very optimistic timeline, ICANN is notoriously slow and bureacratic.
Custom sub-domains (subdomains*.ic0.app) could be the way to forward in the meantime. Perhaps with a process for Dfinity approved custom sub-domain holders having rights to the matching .icp when it is live (to give some continuity in naming).
Other considerations include whether .ICP would be the right string to apply for and also whether ic0.app is the right root domain for the custom sub-domains (removing any barriers to adoption should be the key).
Note: The domain ic.app is already registered (Jan 2021) and it’s unclear whether this is owned by Dfinity. Not criticising the choice of ic0 but ic would have been ideal as the root for sub-domains (avoiding the 0). Although I don’t know enough about IC’s structure how big a change this would be. Or whether ic.app (or some other IC root) could be run in parallel to ic0.app.