Gandalf dies for the Fellowship (representatives of all the peoples of Middle Earth) and is Resurrected and given new powers. He even rides a white horse, wields a sword, and leads an unlooked for host of warriors in the Battle of Helms Deep.
Frodo takes the Ring (the sins of the world) onto himself and suffers and sacrifices all that he loves for the world.
Aragorn is the forseen King who establishes his domain on (Middle-)Earth and sets up a rule of peace and tranquility.
There are also some other interesting insights into Tolkein's Theology. I am personally in awe of his reconciliation of "grace and works" in the story. The "works" of destroying the ring are essential for the "grace" to take effect. Frodo cannot destroy the ring of his own choice, it is left to Providence to destroy it. But that hope of Providence had to be brought about by works.
Without the works, the grace was empty. The Ring would have sat at Rivendell as Sauron overwhelmed Middle-Earth with evil.
Without the grace, the works were empty. Frodo would have been taken by evil and would have become the new Dark Lord, overwhelming Middle-Earth with evil.
Thank you for your insights. If prophet, priest and king then the Fellowship may also represent in some form the trinity acting with angel and man.
“There are three Christ figures in The Lord of the Rings. Prophet (Gandalf), Priest (Frodo), and King (Aragorn).”
...And inderectly, a reference to the Christian Trinity.
Sam Wise. Frodos disciple. When Frodo leaves, he is his representative on Earth.
Frodo does suffer a great deal to return the ring into the fire from which it came. But when that moment comes, he desires to keep the ring for himself. His friend Sam steps forth to throw the ring into the fire. Sam was there to serve and protect Frodo. But he didn't carry the weight or the temptation of the ring. Frodo did that for him. And at last Sam overcomes his fear and must throw the ring in the fire for Frodo who has succumbed to temptation after all his efforts to resist it.