Jer 36:26-27 I will give you a new heart and put a new spirit within you; I will take the heart of stone out of your flesh and give you a heart of flesh. I will put My Spirit within you and cause you to walk in My statutes, and you will keep My judgments and do them.
In the OT, the Spirit of God or the Holy Spirit were given to the Jews for anointing, empowering, gifts, seal of salvation, etc. Even the empowering of the Holy Spirit was not good enough to help his people (Jews) repent and overcome their great wickedness.
1. I will put My Spirit within you
So in this new covenant, on top of the Holy Spirit for salvation, God will also give His people a New Spirit so that they will be empowered with knowledge, understanding and truth of His words, will, teachings.
2. to walk in His statues
John 5:19-20 Then Jesus answered and said to them, "Most assuredly, I say to you, the Son can do nothing of Himself, but what He sees the Father do; for whatever He does, the Son also does in like manner. For the Father loves the Son, and shows Him all things that He Himself does; and He will show Him greater works than these, that you may marvel.
Whatever our Lord Jesus saw or heard from the Father, He will completely obey them by teaching, practicing or performing them (i.e His words, will, teachings, works).
3. Keep His judgement and do them
John 5:30 "I can of Myself do nothing. As I hear, I judge; and My judgment is righteous, because I do not seek My own will but the will of the Father who sent Me."
Our Lord Jesus judged according to the judgment of God. When we obey His will, our judgment will always be righteous, but if we follow our own will (normally selfishness, worldly, carnal, etc), our judgment will be partial, unacceptable and sinful
4. I will take the heart of stone out of your flesh and give you a heart of flesh
With the New Spirit of truth dwelling in us, He will be able to teach us His words and guide us into all truth. The truth will set us free worldliness, rebellion and selfishness. The Spirit of truth will also fill us with the fruit of the Spirit (love, joy, peace, kindness, mercy, long-suffering, etc.)
Spirit of Christ
Mat 20:18-19 "Behold, we are going up to Jerusalem, and the Son of Man will be betrayed to the chief priests and to the scribes; and they will condemn Him to death, and deliver Him to the Gentiles to mock and to scourge and to crucify. And the third day He will rise again."
Christ came in the flesh, suffered humiliation, stripes, chastisements, and was crucified. Having overcame death the Spirit of Christ resurrected Him, so that all godly Christians with the Spirit of Christ will be be able to overcome all trials, temptations, sufferings and even martyrdom.
Rom 8:9-11 But you are not in the flesh but in the Spirit, if indeed the Spirit of God dwells in you. Now if anyone does not have the Spirit of Christ, he is not His. And if Christ is in you, the body is dead because of sin, but the Spirit is life because of righteousness. But if the Spirit of Him who raised Jesus from the dead dwells in you, He who raised Christ from the dead will also give life to your mortal bodies through His Spirit who dwells in you.
1Cor 2:15 But he who is spiritual judges all things, yet he himself is rightly judged by no one.
Brethren, just like our Lord Jesus and His Apostles, all those baptized with the Spirit of Christ must teach truth and to judge and expose the wrong doctrines and heresies in churches.