For - being ignorant of God's righteousness - Not knowing God's method of saving sinners, which is the only proper and efficient method: and going about to establish their own righteousness - seeking to procure their salvation by means of their own contriving; they have not submitted - they have not bowed to the determinations of the Most High, relative to his mode of saving mankind, viz. through faith in Jesus Christ, as the only available sacrifice for sin - the end to which the law pointed.

God's righteousness. 'God's method of justification,' says Abp. Newcome: God's method of saving sinners.'

Romans 1:17 For therein is the righteousness of God revealed from faith to faith: as it is written, The just shall live by faith.

Romans 3:22,26 Even the righteousness of God which is by faith of Jesus Christ to all and on all them that believe: for there is no difference...

Romans 5:19 For as by one man's disobedience many were made sinners, so by the obedience of one shall many be made righteous.

Romans 9:30 What shall we say then? That the Gentiles, which followed not after righteousness, have attained to righteousness...

Psalm 71:15,16,19 My mouth shall show forth your righteousness and your salvation all the day; for I know not the numbers thereof...

Isaiah 51:6,8 Lift up your eyes to the heavens, and look on the earth beneath: for the heavens shall vanish away like smoke...

Isaiah 56:1 Thus said the LORD, Keep you judgment, and do justice: for my salvation is near to come, and my righteousness to be revealed.

Jeremiah 23:5,6 Behold, the days come, said the LORD, that I will raise to David a righteous Branch, and a King shall reign and prosper...

Daniel 9:24 Seventy weeks are determined on your people and on your holy city, to finish the transgression, and to make an end of sins...

John 16:9,10 Of sin, because they believe not on me...

2 Corinthians 5:21 For he has made him to be sin for us, who knew no sin; that we might be made the righteousness of God in him.

2 Peter 1:1 Simon Peter, a servant and an apostle of Jesus Christ...

to establish.

Romans 9:31,32 But Israel, which followed after the law of righteousness, has not attained to the law of righteousness...

Isaiah 57:12 I will declare your righteousness, and your works; for they shall not profit you.

Isaiah 64:6 But we are all as an unclean thing, and all our righteousnesses are as filthy rags; and we all do fade as a leaf; and our iniquities...

Luke 10:29 But he, willing to justify himself, said to Jesus, And who is my neighbor?

Luke 16:15 And he said to them, You are they which justify yourselves before men; but God knows your hearts...

Luke 18:9-12 And he spoke this parable to certain which trusted in themselves that they were righteous, and despised others...

Galatians 5:3,4 For I testify again to every man that is circumcised, that he is a debtor to do the whole law...

Philippians 3:9 And be found in him, not having my own righteousness, which is of the law, but that which is through the faith of Christ...

Revelation 3:17,18 Because you say, I am rich, and increased with goods, and have need of nothing; and know not that you are wretched, and miserable...

submitted.

Leviticus 26:41 And that I also have walked contrary to them, and have brought them into the land of their enemies...

Nehemiah 9:33 However, you are just in all that is brought on us; for you have done right, but we have done wickedly:

Job 33:27 He looks on men, and if any say, I have sinned, and perverted that which was right, and it profited me not;

Lamentations 3:22 It is of the LORD's mercies that we are not consumed, because his compassions fail not.

Daniel 9:6-9 Neither have we listened to your servants the prophets, which spoke in your name to our kings, our princes, and our fathers...

Luke 15:17-21 And when he came to himself, he said, How many hired servants of my father's have bread enough and to spare, and I perish with hunger!...

Christ the End of the Law
The reason why many do not come to Christ is not because they are not earnest, after a fashion, and thoughtful and desirous to be saved, but because they cannot brook God's way of salvation. "They have a zeal for God, but not according to knowledge," We do get them by our exhortation so far on the way that they become desirous to obtain eternal life, but "they have not submitted themselves to the righteousness of God." Mark, "submitted themselves," for it needs submission. Proud man wants to save …
Charles Haddon Spurgeon—Spurgeon's Sermons Volume 22: 1876

Which Sentence Dishonoreth the Holy Martyrs, Nay Rather Taketh Away Holy Martyrdoms Altogether. ...
3. Which sentence dishonoreth the holy Martyrs, nay rather taketh away holy martyrdoms altogether. For they would do more justly and wisely, according to these men, not to confess to their persecutors that they were Christians, and by confessing make them murderers: but rather by telling a lie, and denying what they were, should both themselves keep safe the convenience of the flesh and purpose of the heart, and not allow those to accomplish the wickedness which they had conceived in their mind. …
St. Augustine—Against Lying

Or Haply is it So, that He who Plots in this Way to Find...
13. Or haply is it so, that he who plots in this way to find out Priscillianists, denies not Christ, forasmuch as with his mouth he utters what with his heart he believes not? As if truly (which I also said a little above) when it was said, "With the heart man believeth unto righteousness," it was added to no purpose, "with the mouth confession is made unto salvation?" [2398] Is it not so that almost all who have denied Christ before the persecutors, held in their heart what they believed of Him? …
St. Augustine—Against Lying