How do I recover an old iCloud contact numbers while currently signed in under a new iCloud account?

Sign into the older Apple ID on a device, ensure that the contacts are enabled and present, shut off contacts from the Apple ID, choose keep the data, then connect to the newer Apple ID, enable contacts, and merge the data.

Or set up the old Apple ID as an account and access the contacts directly.

Here are a couple of more-detailed threads on transferring data from one Apple ID to another:

https://discussions.apple.com/thread/250056638

Apple ID - Apple Community