Thank you for your question.
Peter is speaking metaphorically. It is clear from other scriptures that the physical heavens and earth will remain. What will be ‘burned up’ or destroyed is evil men and their works both rulers ‘the heavens’ and the ruled ‘the earth’.
Isaiah 65:17-25 For, behold, I create new heavens and a new earth: and the former shall not be remembered, nor come into mind. But be ye glad and rejoice for ever in that which I create: for, behold, I create Jerusalem a rejoicing, and her people a joy. And I will rejoice in Jerusalem, and joy in my people: and the voice of weeping shall be no more heard in her, nor the voice of crying. There shall be no more thence an infant of days, nor an old man that hath not filled his days: for the child shall die an hundred years old; but the sinner being an hundred years old shall be accursed. And they shall build houses, and inhabit them; and they shall plant vineyards, and eat the fruit of them. They shall not build, and another inhabit; they shall not plant, and another eat: for as the days of a tree are the days of my people, and mine elect shall long enjoy the work of their hands. They shall not labour in vain, nor bring forth for trouble; for they are the seed of the blessed of the LORD, and their offspring with them. And it shall come to pass, that before they call, I will answer; and while they are yet speaking, I will hear. The wolf and the lamb shall feed together, and the lion shall eat straw like the bullock: and dust shall be the serpent’s meat. They shall not hurt nor destroy in all my holy mountain, saith the LORD.
Israel will still exist as a mortal population in the ‘new heavens and earth’ and people will go up to Jerusalem to worship God.
Isaiah 66:22,23 For as the new heavens and the new earth, which I will make, shall remain before me, saith the LORD, so shall your seed and your name remain. And it shall come to pass, that from one new moon to another, and from one sabbath to another, shall all flesh come to worship before me, saith the LORD.
God will send Jesus Christ to establish the kingdom of God on this earth.
Acts 3:20,21 And he shall send Jesus Christ, which before was preached unto you: Whom the heaven must receive until the times of restitution of all things, which God hath spoken by the mouth of all his holy prophets since the world began.
Luke 1:32 He shall be great, and shall be called the Son of the Highest: and the Lord God shall give unto him the throne of his father David:
Daniel 2:44 And in the days of these kings shall the God of heaven set up a kingdom, which shall never be destroyed: and the kingdom shall not be left to other people, but it shall break in pieces and consume all these kingdoms, and it shall stand for ever.
The apostles will govern the twelve tribes of Israel.
Matthew 19:28 And Jesus said unto them, Verily I say unto you, That ye which have followed me, in the regeneration when the Son of man shall sit in the throne of his glory, ye also shall sit upon twelve thrones, judging the twelve tribes of Israel.
The reward of the righteous is eternal life on this earth.
Psalms 37:9 For evildoers shall be cut off: but those that wait upon the LORD, they shall inherit the earth.
Psalms 37:11 But the meek shall inherit the earth; and shall delight themselves in the abundance of peace.
Psalms 37:22 For such as be blessed of him shall inherit the earth; and they that be cursed of him shall be cut off.
This Jesus confirms
Matthew 5:5 Blessed are the meek: for they shall inherit the earth.
The purpose of God is to fill this earth with his glory in the form of a glorified population with the divine nature.
Numbers 14:21 But as truly as I live, all the earth shall be filled with the glory of the LORD.
Isaiah 45:18 For thus saith the LORD that created the heavens; God himself that formed the earth and made it; he hath established it, he created it not in vain, he formed it to be inhabited: I am the LORD; and there is none else.
The righteous shall reign on this earth over a mortal population for a thousand years after which God will dwell with men and be all in all.
Revelation 5:10 And hast made us unto our God kings and priests: and we shall reign on the earth.
Revelation 20:4 ...and they lived and reigned with Christ a thousand years.
Paul sums up.
1 Corinthians 15:22-28 For as in Adam all die, even so in Christ shall all be made alive. But every man in his own order: Christ the firstfruits; afterward they that are Christ’s at his coming. Then cometh the end, when he shall have delivered up the kingdom to God, even the Father; when he shall have put down all rule and all authority and power. For he must reign, till he hath put all enemies under his feet. The last enemy that shall be destroyed is death. For he hath put all things under his feet. But when he saith all things are put under him, it is manifest that he is excepted, which did put all things under him. And when all things shall be subdued unto him, then shall the Son also himself be subject unto him that put all things under him, that God may be all in all.
If we want to have a part in the ‘new heavens and new earth’ we need to understand and obey the gospel.
Mark 16:15,16 And he said unto them, Go ye into all the world, and preach the gospel to every creature. 16 He that believeth and is baptized shall be saved...
I hope this helps.
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