Connecting to an SQL server on a different domain

I am in the process of beuilding a new domain with new Domain Controller and a new Terminal Server that will eventually replace our existing domain which was never really set up properly some years ago before I took over the network. We currently have an SQL Server attaced to our old domain that runs all our databases and what I would like to do is keep it there for testing.

I'm assuming I will have to create some kind of relationship between the SQL Server and the new Terminal Server but we all know what assuming can do.

Any advice on how to proceed would be greatly appreciated.