According to Paul, the Spirit of Christ is the motivating power in the believer's life.  The Spirit is the replacement for the Law, but whereas the Law brought condemnation (2 Cor 3:9), the Spirit gives us life and freedom:

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           Not that we are competent in ourselves to claim anything for ourselves, but our competence comes from God.  He has made us competent as ministers of a new covenant—not of the letter but of the Spirit; for the letter kills, but the Spirit gives life (2 Cor 3:5-6).

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           Now the Lord is the Spirit, and where the Spirit of the Lord is, there is freedom.  And we, who with unveiled faces all reflect the Lord’s glory, are being transformed into his likeness with ever-increasing glory, which comes from the Lord, who is the Spirit (2 Cor 3:17-18).

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The Old Covenant was a three-step recipe: 1. faithful obedience to "the letter."  2. the remedy for failure to obey was to offer a sacrifice.  3. Go back to step 1, but try harder.  This recipe was the life-pattern of the observant Jew.  The goal was to become a holy people, set apart for fellowship with God.  Underneath it all was the assumption that men could follow the instructions.  They certainly weren't hard to understand: do this, don't do that.  But as Paul said, "the letter kills."  I do not believe this is primarily a theological statement, although it has become that.  It was actually existential -- he was speaking as a reformed Pharisee, a man who had zealously followed the recipe for many years, but failed to attain either holiness or fellowship with God.

          

Contrast the assumption of the Law, that man has the power to obey, with Paul's statement in 2 Cor 3:5 -- "we are not competent in ourselves to claim anything"!   What a comedown.  What a setback for the self-esteem bandwagon.  This does not, however, lead him to despair or cynicism.  "Our competence comes from God."  That doesn't appear to make sense -- God was the problem in the first case, He is the One whom the recipe of the Law was attempting to appease.  But for Paul, the righteousness of faith bestows the acceptance with God that he strained to achieve previously.  It also institutes a new recipe:  1. believe in the Lord Jesus Christ as my righteousness.  2. receive the Spirit's presence and guidance, 3. get free from bondage, grow into the likeness of Christ.  4. Go back to step 1.  This is the pattern found in 2 Cor 3:17-18.  Like the Law, it is a life-long pattern, not a one-shot experience.  But the fruit of it is "ever-increasing glory," and not frustration and defeat.