God’s definition of righteousness does not fundamentally change between the old and new testaments of the Bible. Both involve active faith and love for God.
[Deuteronomy 6:4-5 NKJV]:
4 “Hear, O Israel: The LORD our God, the LORD is one!
5 You shall love the LORD your God with all your heart, with all your soul, and with all your strength.
19 I call heaven and earth to witness against you today, that I have set before you life and death, blessing and curse. Therefore choose life, that you and your offspring may live,
20 loving the LORD your God, obeying his voice and holding fast to him, for he is your life and length of days, that you may dwell in the land that the LORD swore to your fathers, to Abraham, to Isaac, and to Jacob, to give them.”
And if it seems evil to you to serve the LORD, choose for yourselves this day whom you will serve, whether the gods which your fathers served that were on the other side of the River, or the gods of the Amorites, in whose land you dwell. But as for me and my house, we will serve the LORD.
Then you shall return, and you will discern between the righteous and the wicked, between one who serves God and one who does not serve Him.
His lord said to him, “Well done, good and faithful servant; you were faithful over a few things, I will make you ruler over many things. Enter into the joy of your lord.’
29 Jesus answered him, “The first of all the commandments is: ‘Hear, O Israel, the LORD our God, the LORD is one.
30 And you shall love the LORD your God with all your heart, with all your soul, with all your mind, and with all your strength.’ This is the first commandment.
31 And the second, like it, is this: “You shall love your neighbor as yourself.’ There is no other commandment greater than these.”
23 Jesus answered him, “If anyone loves me, he will keep my word, and my Father will love him, and we will come to him and make our home with him.
24 Whoever does not love me does not keep my words. And the word that you hear is not mine but the Father’s who sent me.
[1 John 2:3-4]:
3 Now by this we know that we know Him, if we keep His commandments.
4 He who says, “I know Him,” and does not keep His commandments, is a liar, and the truth is not in him.
Jesus said that He is the way, the truth and the life (John 14:6). You cannot separate the life of Jesus (salvation) from his teachings (the truth & the way). Recall Peter’s response to Jesus immediately after He taught that one must abide in Him to be His disciple which caused many to leave. He said “Lord, to whom shall we go? You have the words of eternal life.” (John 6:68) Indeed, Jesus is called the Word of God (John 1:1).
No. God did not change His nature at any point in the Bible. “For I am the LORD, I do not change;” (Malachi 3:6)
Instead, He decided to extend His favor from one people group, Israel, to the entire world (Isaiah 11:10; Hosea 2:23; Ephesians 2:11-18). To greatly aid everyone in choosing life & obeying His commandments He has provided direct access to His power:
[John 14:15-16, 26]:
15 If you love Me, keep My commandments.
16 And I will pray the Father, and He will give you another Helper, that He may abide with you forever
26 But the Helper, the Holy Spirit, whom the Father will send in My name, He will teach you all things, and bring to your remembrance all things that I said to you.
And we are His witnesses to these things, and so also is the Holy Spirit whom God has given to those who obey Him.
[2 Peter 1:2-4]:
2 Grace and peace be multiplied to you in the knowledge of God and of Jesus our Lord,
3 as His divine power has given to us all things that pertain to life and godliness, through the knowledge of Him who called us by glory and virtue,
4 by which have been given to us exceedingly great and precious promises, that through these you may be partakers of the divine nature, having escaped the corruption that is in the world through lust.
Make no mistake — we are saved by grace! Out of an abundance of faithful loving-kindness (Hebrew word: chesed) God incarnated His own Divine substance who properly instructed us (John 1:18; Hebrews 1:1-4), defeated the powers of darkness (Colossians 1:13-14), released us from all bondage (Romans 6:22, Romans 8:15, 2 Corinthians 3:17, Galatians 5:1), cleansed us through His blood (Hebrews 9:14, 1 John 1:7) and granted to us who believe His resurrection Spirit!!!