In his commentary on the weekly Torah portion “Vayakel” (35:1), the Ramban (Nachmonides) writes that the Almighty established with Moses (even before Moses descended from Mount Sinai after his third visit) a “Brit Hadash”, literally “a new union, a covenant.”
With this act, G-d was displaying favor toward the Jewish people by giving them the Second set of Tablets, agreeing to dwell among them, and returning to His original love for them.
So if someone walks up to you on the street with words about a "new covenant", we can justifiably say that we have one! Only ours has nothing to do with what the Christians call the “New Testament”. Of course while saying that, we need to be mindful of the reasons for such a statement.