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(All quotations from the King James Authorised translation unless stated otherwise).
There are not many more details to give. Elijah appeared with Moses and Jesus in the vision of the kingdom of God (Matthew 17:1-3). The Jews neither understood the Law nor the Prophets. The disciples also had problems.
Luke 24:25 Then he said unto them, O fools, and slow of heart to believe all that the prophets have spoken: 26 Ought not Christ to have suffered these things, and to enter into his glory? 27 And beginning at Moses and all the prophets, he expounded unto them in all the scriptures the things concerning himself.
Elijah represents the prophets in the same way that Moses represents the Law.
Malachi 4:5 Behold, I will send you Elijah the prophet before the coming of the great and dreadful day of the LORD: 6 And he shall turn the heart of the fathers to the children, and the heart of the children to their fathers, lest I come and smite the earth with a curse.
It is a matter of what Malachi means by turning the heart of the fathers to the children and the heart of the children to their fathers. The message of John Baptist, who came in the spirit and power of Elijah, was that of repentance from their evil way of life to bring forth fruit in righteousness
The angel Gabriel quotes it thus:
Luke 1:17 And he shall go before him in the spirit and power of Elias, to turn the hearts of the fathers to the children, and the disobedient to the wisdom of the just; to make ready a people prepared for the Lord.
John’s message was clear
Matthew 3:1 In those days came John the Baptist, preaching in the wilderness of Judaea, 2 And saying, Repent ye: for the kingdom of heaven is at hand. 3 For this is he that was spoken of by the prophet Esaias, saying, The voice of one crying in the wilderness, Prepare ye the way of the Lord, make his paths straight... 5 Then went out to him Jerusalem, and all Judaea, and all the region round about Jordan, 6 And were baptized of him in Jordan, confessing their sins. 7 But when he saw many of the Pharisees and Sadducees come to his baptism, he said unto them, O generation of vipers, who hath warned you to flee from the wrath to come? 8 Bring forth therefore fruits meet for repentance: 9 And think not to say within yourselves, We have Abraham to our father: for I say unto you, that God is able of these stones to raise up children unto Abraham. 10 And now also the axe is laid unto the root of the trees: therefore every tree which bringeth not forth good fruit is hewn down, and cast into the fire.
From Matthew 3:3 we see that Elijah’s mission is spoken of in Isaiah 40.
Isaiah 40:1 Comfort ye, comfort ye my people, saith your God. 2 Speak ye comfortably to Jerusalem, and cry unto her, that her warfare is accomplished, that her iniquity is pardoned: for she hath received of the LORD’S hand double for all her sins. 3 The voice of him that crieth in the wilderness, Prepare ye the way of the LORD, make straight in the desert a highway for our God. 4 Every valley shall be exalted, and every mountain and hill shall be made low: and the crooked shall be made straight, and the rough places plain: 5 And the glory of the LORD shall be revealed, and all flesh shall see it together: for the mouth of the LORD hath spoken it. 6 The voice said, Cry. And he said, What shall I cry? All flesh is grass, and all the goodliness thereof is as the flower of the field: 7 The grass withereth, the flower fadeth: because the spirit of the LORD bloweth upon it: surely the people is grass. 8 The grass withereth, the flower fadeth: but the word of our God shall stand for ever. 9 O Zion, that bringest good tidings, get thee up into the high mountain; O Jerusalem, that bringest good tidings, lift up thy voice with strength; lift it up, be not afraid; say unto the cities of Judah, Behold your God! 10 Behold, the Lord GOD will come with strong hand, and his arm shall rule for him: behold, his reward is with him, and his work before him. 11 He shall feed his flock like a shepherd: he shall gather the lambs with his arm, and carry them in his bosom, and shall gently lead those that are with young.
This would possibly indicate that Elijah comes at the Jews’ lowest ebb when ‘her warfare is accomplished’ in that henceforward God will rescue and restore Israel and Jerusalem. Her warfare was certainly not accomplished or her iniquity pardoned in Jesus’ day for they killed him, but it will be when they respond to Elijah.
Isaiah 41:27 The first shall say to Zion, Behold, behold them: and I will give to Jerusalem one that bringeth good tidings.
Malachi 3:1 Behold, I will send my messenger, and he shall prepare the way before me: and the Lord, whom ye seek, shall suddenly come to his temple, even the messenger of the covenant, whom ye delight in: behold, he shall come, saith the LORD of hosts.
Malachi 4:1 For, behold, the day cometh, that shall burn as an oven; and all the proud, yea, and all that do wickedly, shall be stubble: and the day that cometh shall burn them up, saith the LORD of hosts, that it shall leave them neither root nor branch. 2 But unto you that fear my name shall the Sun of righteousness arise with healing in his wings; and ye shall go forth, and grow up as calves of the stall. 3 And ye shall tread down the wicked; for they shall be ashes under the soles of your feet in the day that I shall do this, saith the LORD of hosts.
The final tribulation of the Jews is recorded in Zechariah 13:
Zechariah 13:8 And it shall come to pass, that in all the land, saith the LORD, two parts therein shall be cut off and die; but the third shall be left therein. 9 And I will bring the third part through the fire, and will refine them as silver is refined, and will try them as gold is tried: they shall call on my name, and I will hear them: I will say, It is my people: and they shall say, The LORD is my God.
Zechariah 14:1 Behold, the day of the LORD cometh, and thy spoil shall be divided in the midst of thee. 2 For I will gather all nations against Jerusalem to battle; and the city shall be taken, and the houses rifled, and the women ravished; and half of the city shall go forth into captivity, and the residue of the people shall not be cut off from the city. 3 Then shall the LORD go forth, and fight against those nations, as when he fought in the day of battle.
That some preparation of the Jews is necessary before they will recognise their Messiah is clear. Exactly when in the order of events Elijah will appear is not clear. His mission will be will be crowned with more success than that of John Baptist.
Zechariah 12:10 And I will pour upon the house of David, and upon the inhabitants of Jerusalem, the spirit of grace and of supplications: and they shall look upon me whom they have pierced, and they shall mourn for him, as one mourneth for his only son, and shall be in bitterness for him, as one that is in bitterness for his firstborn.
There is no other information on the topic that I am aware of that I can give you.
I hope this helps.