I cannot improve on the words of Fr Dwight Longenecker:
At the Transfiguration Christ's glory is revealed to the Apostles in the midst of Elijah and Moses because they were given the same grace: Moses on Mt Sinai, and then Elijah on Mt Horeb (and did you know that Horeb is just another name for Sinai?).
So Elijah went to the same holy mountain where Moses had encountered God. But their epiphanies were complementary. Moses beheld God in the earthquake, fire and thunder on the mountain. Elijah in the still, small voice.
Both pointed to the coming of Christ the Tiger. He who comes with the power and majesty of God, but in the form of the meek and gentle Master. He is both the Lion of Judah and the Lamb of God.