Elijah the prophet was prophecied to return before the day of the Lord (the day Jesus returns at the last day).
Mal 4:5 Behold, I will send you Elijah the prophet before the coming of the great and dreadful day of the LORD:
Elijah did not die, but was taken to heaven in a whirlwind. (2 Kings 2:11)
Elijah appeared with Moses and talked with Jesus...
Mark 9:4 And there appeared unto them Elias with Moses: and they were talking with Jesus.
Elijah is the Old Testament pronunciation, and Elias is the New Testament pronunciation, but it's the same man.
But this was not the "coming" of Elijah.
When John the Baptist was foretold by the angel Gabriel, he told the father of John that his son would come in the spirit and power of Elijah. Not a physical re-incarnation of Elijah, but meaning he shall be such a man as Elias was, and do such work as Elias did, and like Elias, preach the necessity of repentance and reformation to a very corrupt and degenerate age, and will have the same power that Elias did.
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.
The spirit and power of Elias is to turn people to repentance and prepare the way of the Lord. This is exactly what John the Baptist did.
Jesus tells the disciples that indeed, Elijah had come (in spirit and power). It was the prophet's spirit and works that He meant.
Matt 17:12 But I say unto you, That Elias is come already, and they knew him not, but have done unto him whatsoever they listed. Likewise shall also the Son of man suffer of them. 13 Then the disciples understood that he spake unto them of John the Baptist.
Elijah came not as himself, but the "spirit and power" of Elijah came in John the Baptist. This was the fulfillment of the scripture, as Jesus said. It is already fulfilled.
So, Elijah was not reincarnated since he didn't die, but we see it was not even necessary since it was not the actual man Elijah that the Lord spoke of. And, Moses was with Elijah when he was speaking with Jesus. Moses actually died, so how did he appear there with Elijah?
Where is it that those who have died, or were taken to heaven, wait? All those who are gone from this world are in Sheol, which is simply "the place of departed souls" where all wait for the Lord. This is a long subject but I'll try to explain it in a few words. The Bible shows us how there are multiple parts to Sheol, or "hell". This is not to be confused with the lake of fire. Sheol and the lake of fire are NOT the same thing. And there is more than one part of Sheol...
In the Bible, the word "hell" comes from the words "Sheol" (Old Testament) and "Hades" (New Testament).
OT:7585 she'owl (sheh-ole'); or sheol (sheh-ole'); from OT:7592; Hades or the world of the dead (as if a subterranean retreat), including its accessories and inmates:
NT:86 haides (hah'-dace); from NT:1 (as negative particle) and NT:1492; properly, unseen, i.e. "Hades" or the place (state) of departed souls:
NT:5020 tartaroo (tar-tar-o'-o); from Tartaros (the deepest abyss of Hades); to incarcerate in eternal torment:
Tartaroo is where the angels are reserved (the deepest abyss of Hades) for Judgment in 2 Peter 2:4 For if God spared not the angels that sinned, but cast them down to hell (Tartaroo), and delivered them into chains of darkness, to be reserved unto judgment;
As we see, there is more than one "level" or "part" to Sheol. It's the place of the dead, separated with no way to cross to the other parts, for sinners in some parts and for the saints of God in the good part.
The book of Enoch adds to what we know from the Bible. In the book of Enoch we learn that Sheol has 4 parts and one of those parts is where the righteous departed souls wait in the part in which there is the "bright spring of water". So Elijah and Moses, and all righteous souls are in this good part of Sheol.
In Enoch, we're shown that these 4 different parts of Sheol are for the souls of men to be separated and reserved until Judgment Day. We see that some will "not be slain in the day of judgment nor shall they be raised from thence". These will remain in hell forever.
There is a part "in which there is the bright spring of water" for the righteous dead.
In Enoch chapter 70 we see that Enoch is translated to "the place for the elect", where he saw the "first fathers and the righteous who from the beginning dwell". Enoch and Elijah were both taken to the good part of Sheol where the righteous are all resting and waiting for the Day of the Lord.
So all those who have died are in one part or another of Sheol, waiting for the Lord's day. Some for judgment, and some for everlasting life! I thank you, Lord, for you blood and your grace and mercy, that we might spend eternity with you! Praise your Name!