This was a search in the Bible (ESV) for the phrase “draw near”. I have omitted some verses that I thought were less relevant. Search here for all verses.
Interesting to compare OT to NT. You see the things that prevented people from drawing near to God (blemishes, being an outsider). David calls for God to draw near to him to redeem him. Drawing near is about the heart and about actions, not the mouth and its words. And there is the act of making an offering for atonement. Then in the NT you have Christ who is the perfect offering for the atonement of our sins. Blemishes are no more, for those who draw near are made perfect. Christ is “a better hope” (than ourselves) through which we can draw near to God, with confidence. Yet the admonishments about heart integrity are still there.
Leviticus 9:7 (Show me Leviticus 9)
Then Moses said to Aaron, “Draw near to the altar and offer your sin offering and your burnt offering and make atonement for yourself and for the people, and bring the offering of the people and make atonement for them, as the Lord has commanded.”
Numbers 16:40 (Show me Numbers 16)
to be a reminder to the people of Israel, so that no outsider, who is not of the descendants of Aaron, should draw near to burn incense before the Lord, lest he become like Korah and his company—as the Lord said to him through Moses.
1 Samuel 14:36 (Show me 1 Samuel 14)
Then Saul said, “Let us go down after the Philistines by night and plunder them until the morning light; let us not leave a man of them.” And they said, “Do whatever seems good to you.” But the priest said, “Let us draw near to God here.”
Ecclesiastes 5:1 (Show me Ecclesiastes 5)
 Guard your steps when you go to the house of God. To draw near to listen is better than to offer the sacrifice of fools, for they do not know that they are doing evil.
Ch 4:17 in Hebrew
Isaiah 29:13 (Show me Isaiah 29)
And the Lord said: “Because this people draw near with their mouth and honor me with their lips, while their hearts are far from me, and their fear of me is a commandment taught by men,
Isaiah 41:1 (Show me Isaiah 41)
Fear Not, For I Am with You
Listen to me in silence, O coastlands; let the peoples renew their strength; let them approach, then let them speak; let us together draw near for judgment.
Isaiah 45:20 (Show me Isaiah 45)
“Assemble yourselves and come; draw near together, you survivors of the nations! They have no knowledge who carry about their wooden idols, and keep on praying to a god that cannot save.
Isaiah 48:16 (Show me Isaiah 48)
Draw near to me, hear this: from the beginning I have not spoken in secret, from the time it came to be I have been there.” And now the Lord God has sent me, and his Spirit.
Isaiah 58:2 (Show me Isaiah 58)
Yet they seek me daily and delight to know my ways, as if they were a nation that did righteousness and did not forsake the judgment of their God; they ask of me righteous judgments; they delight to draw near to God.
Jeremiah 30:21 (Show me Jeremiah 30)
Their prince shall be one of themselves; their ruler shall come out from their midst; I will make him draw near, and he shall approach me, for who would dare of himself to approach me? declares the Lord.
Ezekiel 43:19 (Show me Ezekiel 43)
you shall give to the Levitical priests of the family of Zadok, who draw near to me to minister to me, declares the Lord God, a bull from the herd for a sin offering.
Malachi 3:5 (Show me Malachi 3)
“Then I will draw near to you for judgment. I will be a swift witness against the sorcerers, against the adulterers, against those who swear falsely, against those who oppress the hired worker in his wages, the widow and the fatherless, against those who thrust aside the sojourner, and do not fear me, says the Lord of hosts.
Hebrews 7:25 (Show me Hebrews 7)
Consequently, he is able to save to the uttermost those who draw near to God through him, since he always lives to make intercession for them.
That is, completely; or at all times
Hebrews 10:1 (Show me Hebrews 10)
Christ’s Sacrifice Once for All
For since the law has but a shadow of the good things to come instead of the true form of these realities, it can never, by the same sacrifices that are continually offered every year, make perfect those who draw near.