Clearly, the New Covenant is not merely future, but past, present, and future ~ since Jesus's coming and coming to completeness at His return. This is God's infallible and inerrant Word (emphases added):
Just for completeness's sake, here is the New Covenant that God promises through Jeremiah:
“Behold, the days are coming, declares the LORD, when I will make a new covenant with the house of Israel and the house of Judah, not like the covenant that I made with their fathers on the day when I took them by the hand to bring them out of the land of Egypt, my covenant that they broke, though I was their husband, declares the LORD. For this is the covenant that I will make with the house of Israel after those days, declares the LORD: I will put my law within them, and I will write it on their hearts. And I will be their God, and they shall be my people. And no longer shall each one teach his neighbor and each his brother, saying, ‘Know the LORD,’ for they shall all know me, from the least of them to the greatest, declares the LORD. For I will forgive their iniquity, and I will remember their sin no more.” (Jeremiah 31:31-34)
What Jesus did and taught throughout His public ministry, even from the beginning when He read from Isaiah 9 and 61, confirms this. Matthew and Luke document this, but here is the text of
“The Spirit of the Lord is upon Me, because He has anointed Me to proclaim good news to the poor. He has sent Me to proclaim liberty to the captives and recovering of sight to the blind, to set at liberty those who are oppressed, to proclaim the year of the Lord’s favor.” (Luke 4:18-19)
Paul says has been happening since Jesus came, and is still the case even today:
Regarding God's putting His law within us, and writing it on our hearts:
"For when Gentiles, who do not have the law, by nature do what the law requires, they are a law to themselves, even though they do not have the law. They show that the work of the law is written on their hearts... For no one is a Jew who is merely one outwardly, nor is circumcision outward and physical. But a Jew is one inwardly, and circumcision is a matter of the heart, by the Spirit, not by the letter. His praise is not from man but from God." (Romans 2:14-15; Romans 2:28-29).
"God’s love has been poured into our hearts through the Holy Spirit who has been given to us" (Romans 5:5)
"But thanks be to God, that you who were once slaves of sin have become obedient from the heart to the standard of teaching to which you were committed..." (Romans 6:17)
And it is God who establishes us with you in Christ, and has anointed us, and who has also put his seal on us and given us his Spirit in our hearts as a guarantee." (2 Corinthians 1:21-22)
"And you show that you are a letter from Christ delivered by us, written not with ink but with the Spirit of the living God, not on tablets of stone but on tablets of human hearts." (2 Corinthians 3:3)
"But when the fullness of time had come, God sent forth His Son, born of woman, born under the law, to redeem those who were under the law, so that we might receive adoption as sons. And because you are sons, God has sent the Spirit of his Son into our hearts, crying, “Abba! Father!” So you are no longer a slave, but a son, and if a son, then an heir through God." (Galatians 4:4-7)
"For this reason, because I have heard of your faith in the Lord Jesus and your love toward all the saints, I do not cease to give thanks for you, remembering you in my prayers, that the God of our Lord Jesus Christ, the Father of glory, may give you the Spirit of wisdom and of revelation in the knowledge of him, having the eyes of your hearts enlightened, that you may know what is the hope to which he has called you, what are the riches of his glorious inheritance in the saints, and what is the immeasurable greatness of his power toward us who believe, according to the working of his great might..." (Ephesians 1:15-19)
"For this reason I bow my knees before the Father, from Whom every family in heaven and on earth is named, that according to the riches of His glory He may grant you to be strengthened with power through his Spirit in your inner being, so that Christ may dwell in your hearts through faith..." (Ephesians 3:14-17)
"Now may our God and Father himself, and our Lord Jesus, direct our way to you, and may the Lord make you increase and abound in love for one another and for all, as we do for you, so that He may establish your hearts blameless in holiness before our God and Father, at the coming of our Lord Jesus with all his saints." (1 Thessalonians 3:11-13)
Regarding His forgiving our sins and remembering them ~ exacting condemnation and judgment because of our sin ~ no more:
"There is therefore now no condemnation for those who are in Christ Jesus. For the law of the Spirit of life has set you free in Christ Jesus from the law of sin and death. For God has done what the law, weakened by the flesh, could not do. By sending his own Son in the likeness of sinful flesh and for sin, he condemned sin in the flesh, in order that the righteous requirement of the law might be fulfilled in us, who walk not according to the flesh but according to the Spirit." (Romans 8:1-4)
"In (Christ Jesus) we have redemption through His blood, the forgiveness of our trespasses, according to the riches of his grace..." (Ephesians 1:7)
"Be kind to one another, tenderhearted, forgiving one another, as God in Christ forgave you." (Ephesians 4:32)
"...thanks to the Father, Who has qualified you to share in the inheritance of the saints in light. He has delivered us from the domain of darkness and transferred us to the kingdom of his beloved Son, in Whom we have redemption, the forgiveness of sins." (Colossians 1:12-14)
"...if we walk in the light, as He is in the light, we have fellowship with one another, and the blood of Jesus his Son cleanses us from all sin. If we say we have no sin, we deceive ourselves, and the truth is not in us. If we confess our sins, He is faithful and just to forgive us our sins and to cleanse us from all unrighteousness." (1 John 1:7-9)
Again, without question, the New Covenant is not merely future, but past, present, and future ~ since Jesus's coming and coming to completeness at His return. It is firmly in place, the one everlasting Covenant having finally blossomed in it's glorious fullness,
encompassing all the previous lesser covenants which all fall under the heading of the Old Covenant (the covenant of life with Adam and renewed with Noah, the covenant of a people and land with Abraham, the covenant of the law with Moses, the covenant of forever kingship with David).
Jesus Christ is the final, perfect, complete iteration of God's Covenant made through Jesus in His life, death, resurrection, and ascension to the the right hand of the Father and in the pouring out of His Spirit, a very present reality. We have this now, and it will be made complete in the fullness of God's time, His millennium, at Christ's return. As Paul says:
"Lest you be wise in your own sight, I do not want you to be unaware of this mystery, brothers: a partial hardening has come upon Israel, until the fullness of the Gentiles has come in. And in this way all Israel will be saved..." (Romans 11:25-27)
Grace and peace to all!