I believe Jesus' mention of the new covenant corresponds to the one described by the writer of Hebrews - the end of the Mosaic covenant/Levitical priesthood (an old administration of the covenant of grace), and the commencement of "a better covenant (8:6)" that actually predates Moses, the "order of Melchizakek (6:20)." A new administration of the covenant of grace. Substance replaces the obsolete types and shadows.

-Robin