Hi @MrEco-9773,
The process for moving Azure AD Connect to a new server: compare configurations of the old and new servers, add AAD Connect on a new server, enable staging mode on it, remove AAD Connect from the old server, and disable staging mode on the new one.
As for migrating ADFS, if it is a farm then you can add an additional ADFS server as a secondary one and then make it primary: http://social.technet.microsoft.com/wiki/contents/articles/1432.ad-fs-2-0-how-to-set-the-primary-federation-server-in-a-wid-farm.aspx
Once done, you can remove the other server.
If it is standalone, you can refer to these guides: