Yes, Jesus established the new covenant.[Luk 22:20 NIV] 20 In the same way, after the supper he took the cup, saying, “This cup is the new covenant in my blood, which is poured out for you. [Heb 8:6 NIV] 6 But in fact the ministry Jesus has received is as superior to theirs as the covenant of which he is mediator is superior to the old one, since the new covenant is established on better promises. [Heb 12:24 NIV] 24 to Jesus the mediator of a new covenant, and to the sprinkled blood that speaks a better word than the blood of Abel.
Even the Jews do not follow the Mosaic covenant, in particular the Levitical laws of the sacrificial system. So, what has to replace that? For the Orthodox Jews, they are waiting to rebuild the temple so they can reinstitute it. For the Christians, the Levitical sacrificial system has been replaced by the ultimate sacrifice by Jesus, the lamb of God.
How could he have finished the work without establishing the new covenant?
I already presented passages from the NT he established the new covenant. This was a fulfillment of the passages from Jeremiah:[Jer 31:31-34 NIV] 31 “The days are coming,” declares the LORD, “when I will make a new covenant with the people of Israel and with the people of Judah. 32 It will not be like the covenant I made with their ancestors when I took them by the hand to lead them out of Egypt, because they broke my covenant, though I was a husband to them,” declares the LORD. 33 “This is the covenant I will make with the people of Israel after that time,” declares the LORD. “I will put my law in their minds and write it on their hearts. I will be their God, and they will be my people. 34 No longer will they teach their neighbor, or say to one another, ‘Know the LORD,’ because they will all know me, from the least of them to the greatest,” declares the LORD. “For I will forgive their wickedness and will remember their sins no more.”
Of course Jews do not interpret it this way as the Christians do. But one has to ask the Jews when will God ever forgive their wickedness and sins? Do they have to wait for the Messianic age for this to happen? It’s been a long wait for the Jews and who knows how much longer they still have to wait. How many generations of Jews have lived and died waiting for this to happen and their sins have not been forgiven by God? Instead Jesus came before the second temple was destroyed, so there’s always been a method provided by God for the atonement of sins – either follow the Levitical sacrificial system or accept the sacrifice of Jesus.