Concise Bible Dictionary:
An expression descriptive of a moral condition or order of man which has come into view in Jesus (Eph. 4:21), and the character of which is described in that it is created after God in righteousness and holiness of truth. In His death Christ broke down the wall of partition between Jew and Gentile to create the two in Himself into “one new man,” reconciling both unto God in one body by the cross, there remaining thus as before God no longer Jew or Gentile, but a man of an entirely new order. The new man “stands in contrast to the old man,” which represents the corrupt state by nature of the children of the first man Adam. This having been put off, the believer has also put on “the new man,” the state proper to the Christian—a new creation in Christ. The new man being created is thus entirely new (καινός). In Colossians 3:10 Christians are viewed as having put off the old man with his deeds, it being replaced by the new (νέος) man, which is renewed (άνακαινούμενον) for full knowledge; hence Christ lives in the saints, and His moral traits are developed in life in the one body. Christ is everything (for the old man of every kind is excluded) and is in each saint. For the difference of the two Greek words see NEW.
From Anstey’s Doctrinal Definitions:
This term is found in Ephesians 4:24 and Colossians 3:10. Like the “old man,” the “new man” is an abstract expression. It denotes the new order of moral perfection in the new creation race under Christ. The old man is characterized by being “corrupt” and “deceitful,” but the new man is characterized by “righteousness” and “holiness” (Eph. 4:22-24).
The term “the new man” is often used by Christians as if it were synonymous with the new nature in the believer. This is a widespread misunderstanding among Christians. People will say, "The new man in us needs to feed on Christ." Or, "Our new man needs an Object—Christ." These statements are confusing the new man with the new life and nature in the believer, which definitely does have desires and appetites, and needs an Object. As mentioned, the new man is an abstract term—not a living thing in the believer—denoting the new moral order of perfection in the new creation race. This point was touched on in a periodical years ago: "Is the new man what we are by new birth? No. It is an abstract term standing here in contrast to both Jew and Gentile; it is a completely new order of man taking its character from Christ" (Precious Things, vol. 4, p. 302).
The “new man” first came into view “in Jesus” (Eph. 4:21). That is, men first saw this moral perfection when the Lord walked here in this world as a Man. (“Jesus” is His name as a Man.) Every moral feature of the new man was seen in perfection in Him. As the old man is not Adam personally, so also the new man is not Christ personally. G. Davison said, "The new man is not Christ personally, but it is Christ characteristically" (Precious Things, vol. 3, p. 260).
The emphasis of Paul’s exhortation in the latter verses of Ephesians 4 is that we should put into practice what is true in fact. Since we are Christians, we have put off the “old man” and have put on the “new man”—it is a thing that has been done (Eph. 4:24; Col. 3:10 – J. N. Darby Trans.). Therefore, we are exhorted to be done with that old corrupt lifestyle that marks the old man and live after what characterizes the new man. Paul mentions a number of moral transitions that should naturally result in the life of the believer as he walks in “righteousness and true holiness.” They are:
• Honesty instead of falsehood (vs. 25).
• Unabating righteous anger against evil instead of indifference to it (vss. 26-27).
• Giving to others rather than stealing from them (vs. 28).
• Speaking with grace to others rather than using corrupt communication (vs. 29).
• Kindness rather than bitterness (vss. 31-32).
• Tenderheartedness [compassion] rather than the heat of passion (vss. 31-32).
• Showing grace to others rather than being wrathful, clamorous, injurious, and malicious (vss. 31-32).
In Colossians 3, Paul mentions ten moral characteristics of the “new man” that should be seen in the saints as they exhibit the truth of “Christ in you, the hope of glory” (Col. 1:27):
• Compassion (vs. 12).
• Kindness (vs. 12).
• Lowliness (vs. 12).
• Meekness (vs. 12).
• Longsuffering (vs. 12).
• Forbearance (vs. 13).
• Forgiveness (vs. 13).
• Love (vs. 14).
• Peace (vs. 15).
• Thankfulness (vs. 15).
Since the new man is patterned after “the image of Him who created him,” we being part of the new creation race which has put on the new (Eph. 4:24; Col. 3:10), are fully able to represent God in this world. The moral features of the new man will be seen in us as we “walk in the Spirit” (Gal. 5:22-25).