I am creating a new email domain on our existing Marketo account for communication purposes. Do I have to get this new domain approved on Marketo or is there any other setup required at Marketo to add a new mailing domain apart from the existing domains?
You don't need to get anything "approved" in the manual sense. However, you should set up DKIM for any new domain, as you should have for existing domains. (SPF is optional, unless you have the Branded Sender add-on to your Marketo subscription.)