A new birth is required for entrance into Heaven, as the Lord said "Except a man be born again, he cannot see the kingdom of God" (John 3:3-7).
A person becomes born again as a child of God through simple faith in Jesus Christ as their Savior:
1 John 5:1
1 Whosoever believeth that Jesus is the Christ is born of God: and every one that loveth him that begat loveth him also that is begotten of him.
John 1:12 and Galatians 3:26 also testify to this fact - one is born again into God's family simply by putting their faith in Jesus Christ as their Savior.
When someone believes in Jesus, an entirely new person is born within them, born after the incorruptible seed of God, in distinction from the corrupt flesh of their first birth:
1 Peter 1:23
23 Being born again, not of corruptible seed, but of incorruptible, by the word of God, which liveth and abideth for ever.
This New Man, which is born of God, is incapable of sinning or displeasing God, once again, in distinction from the Old Man of their first birth:
1 John 3:9
9 Whosoever is born of God doth not commit sin; for his seed remaineth in him: and he cannot sin, because he is born of God.
1 John 5:18
18 We know that whosoever is born of God sinneth not; but he that is begotten of God keepeth himself, and that wicked one toucheth him not.
2 Corinthians 5:17
17 Therefore if any man be in Christ, he is a new creature: old things are passed away; behold, all things are become new.
When a believer's physical body dies, only this New Man will remain, which is why believers will have no potential to sin in Heaven. Their new nature is born of God, and incorruptible.
While believers have an new nature, their old nature is still with them. The physical bodies of believers did not get redeemed when they believed. Believers still have the same brain, the same arms, legs, etc. as they did prior salvation. The body of believers will not be redeemed until Jesus Christ returns (Philippians 3:20-21: 1 Corinthians 15:52-53, Romans 8:23).
The two natures present within a believer are in a struggle against each other for dominance over the believer's will, and while they remain in an unglorified body, that will always be the case:
Galatians 5:17
17 For the flesh lusteth against the Spirit, and the Spirit against the flesh: and these are contrary the one to the other: so that ye cannot do the things that ye would.
A believer's choices determine which nature is operative on their will, at any given moment. This is why the New Testament constantly instructs and reminds believers to walk in the Spiritual Nature, the New Man:
Colossians 3:9-10
9 Lie not one to another, seeing that ye have put off the old man with his deeds;
10 And have put on the new man, which is renewed in knowledge after the image of him that created him:
Ephesians 4:22-24
22 That ye put off concerning the former conversation the old man, which is corrupt according to the deceitful lusts;
23 And be renewed in the spirit of your mind;
24 And that ye put on the new man, which after God is created in righteousness and true holiness.
Romans 6:6, 11-13, 16
6 Knowing this, that our old man is crucified with him, that the body of sin might be destroyed, that henceforth we should not serve sin.
11 Likewise reckon ye also yourselves to be dead indeed unto sin, but alive unto God through Jesus Christ our Lord.
12 Let not sin therefore reign in your mortal body, that ye should obey it in the lusts thereof.
13 Neither yield ye your members as instruments of unrighteousness unto sin: but yield yourselves unto God, as those that are alive from the dead, and your members as instruments of righteousness unto God.
16 Know ye not, that to whom ye yield yourselves servants to obey, his servants ye are to whom ye obey; whether of sin unto death, or of obedience unto righteousness?
Romans 12:1-2
1 I beseech you therefore, brethren, by the mercies of God, that ye present your bodies a living sacrifice, holy, acceptable unto God, which is your reasonable service.
2 And be not conformed to this world: but be ye transformed by the renewing of your mind, that ye may prove what is that good, and acceptable, and perfect, will of God.
Romans 13:14
14 But put ye on the Lord Jesus Christ, and make not provision for the flesh, to fulfil the lusts thereof.
Galatians 5:16
16 This I say then, Walk in the Spirit, and ye shall not fulfil the lust of the flesh.
Above, walking in the Old Man is contrasted with the experience of walking in the Spirit, wherein one dies to self, and submits to the Lordship of Jesus Christ. This message of discipleship was taught repeatedly by the Lord during His ministry (Matthew 10:34-39, 16:24-27, Mark 8:34-38, Luke 9:23-26, 14:25-35, John 12:24-25).
In light of the above passages of Scripture, this dying to self, and reckoning one's Old Man dead - that is, not operative on their will - can be said to be a major theme in the New Testament. It is mentioned in dozens of verses of Scripture, and is the principle which guides all doctrine on sanctification in the Christian life after conversion.
Walking in the New Man requires diligent effort on behalf of the believer. If it did not, but were instead automatic, the exhortations that have been discussed so far would be entirely unnecessary.
Notice that the call to discipleship is one of total surrender to Jesus Christ, meaning that the ideal form of discipleship involves total submission:
Luke 14:33
33 So likewise, whosoever he be of you that forsaketh not all that he hath, he cannot be my disciple.
If submitting to the Lordship of Christ, and walking in the New Man, were an automatic feature of every believer's life after the New Birth, such exhortations would be totally unnecessary - yet they abound in the New Testament:
Titus 3:8, 14
8 This is a faithful saying, and these things I will that thou affirm constantly, that they which have believed in God might be careful to maintain good works. These things are good and profitable unto men.
14 And let our's also learn to maintain good works for necessary uses, that they be not unfruitful.
Colossians 2:6
6 As ye have therefore received Christ Jesus the Lord, so walk ye in him:
Colossians 3:2-3, 5
2 Set your affection on things above, not on things on the earth.
3 For ye are dead, and your life is hid with Christ in God.
5 Mortify therefore your members which are upon the earth; fornication, uncleanness, inordinate affection, evil concupiscence, and covetousness, which is idolatry:
Other examples of these exhortations are Philippians 1:27, 2:3, 2:14, 3:1, 3:16, 4:1-2, 4:4-5, 4:8-9, Colossians 3:12-17, 4:6, etc., etc. One could go through each book and probably pick out at least a dozen verses that are exhortations to live righteously, none of which would be required if discipleship an automatic or guaranteed feature of a child of God's life that the Holy Spirit's indwelling alone produced. Walking in the Spirit is a choice made by believers, and it takes effort, work, and sacrifice on their part.
And, "genuine" believers frequently fail in this effort. The Apostle Paul describes his own failures to walk in the New Man in Romans 7:14-8:16, in which he laments over the times in which he yields his will to the Old Man, despite knowing better, and having a desire to serve the Lord. Failure to walk in the New Man does not invalidate the New Birth. It instead means that one needs help in the area of discipleship, or they will squander their chance to earn eternal rewards at the Judgment Seat of Christ (1 Corinthians 3:11-15), and can incur temporal chastening at the hand of their Heavenly Father (Hebrews 12:6).
Therefore, effective discipleship requires consistent and often difficult work on behalf of a believer. And, believers can fail in their journey of discipleship, precisely because it takes work on their behalf.
After the New Birth, in which an entirely new nature is born within believers, believers still retain the unregenerate body of their first birth, born after Adam. This old nature will fight the believer's new nature for dominance over their will, and the success which a believer sees in that battle will be a factor of their own choice to die to self, and submit their will to that which is pleasing to Jesus Christ, which is an expression of their New Man.
A believer's success or failure in this battle is not an infallible means of attaining assurance of Salvation, or signaling who is regenerate or unregenerate, as it will be imperfect, and depends on a believer's effort - work - in submitting to the Lord.