De-Indexing Old Site

Hi,

I recently forwarded an existing domain that was previously being used for a Squarespace site to a new domain and Wordpress site. The issue is the old site is still indexed by Google and the client doesn't really want the old information seen. I still have access to the old Squarespace site and I've set it to private but not sure of the best way of no-indexing the site now?.

Any advice appreciated.

Andy