How is Jesus's teaching in John's Gospel concerning Paraclete deal with the problem of parousia? How is parousia understood in the 21st century?
Paraclete is the Greek term meaning "comforter," and is normally used to describe the presence of the Holy Spirit, the third person of the Trinity. "Parousia," meaning "presence," and normally refers to the second coming of Christ, which he promised in the Gospels.
There is no problem between the two. Jesus indicated the Holy Spirit (Paraclete) would come during his absence from earth to comfort and be an advocate for mankind:
When the Advocate comes, whom I will send to you from the Father —the Spirit of truth who goes out from the Father—he will testify about me. And you also must testify, for you have been with me from the beginning.
The Comforter, or Holy Spirit, was given to the Disciples shortly after Jesus ascension into heaven.
In other passages, Jesus speaks of the signs of his Second Coming, but pointedly states that no one knows when this will be:
But about that day or hour no one knows, not even the angels in heaven, nor the Son, but only the Father....Therefore keep watch, because you do not know on what day your Lord will come.
There have been in the past and today many prophecies of the "end times," yet such prophecies are contradictory to the express words of Jesus that no one knows. There is no problem with the paraclete and the second coming; they are separate and distinct.