Three verbs with similar meanings:
The role of John The Baptist of the New Testament echoes/recalls/evokes that of Elijah the Prophet of the Old Testament.
echo (v.)
To repeat details that are similar to, and make you think of, something else:
The design of the church echoes that of St. Paul's Cathedral.
Cambridge
recall (v.)
To cause you to think of a particular event, situation, or style:
His paintings recall the style of Picasso.
Cambridge
Perhaps somewhatslightly weaker is
evoke (v.)
To cause something to be remembered or expressed
Cambridge
First, John's initial physical description in chapter 3 evokes Elijah.
Kendra Mohn; Masculinities in the Gospel of Matthew Joseph, John, Peter, and Judas (2024)
If you are writing (even a speech or presentation), I would avoid the informal group genitive: "[John The Baptist of the New Testament]'s role" because it can be (mis)read as the role of the New Testament. We get away with this construction in speech when we start a sentence, paint ourselves into a corner, and use the group genitive to save us from restarting and rephrasing. But we should always rewrite to avoid something like "The boy I saw on the corner yesterday's father is my professor."