> The role of John The Baptist of the New Testament **echoes/recalls**
> 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][1]

**recall** (v.)

> To cause you to think of a particular event, situation, or style:
> 
> *His paintings recall the style of Picasso.*  
>[Cambridge][2]

If you are writing, 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 because we start a sentence, paint ourselves in a corner, and the group genitive saves us from rephrasing. But we should rewrite "The boy I saw on the corner's father is my teacher.")


  [1]: https://dictionary.cambridge.org/us/dictionary/english/echo
  [2]: https://dictionary.cambridge.org/us/dictionary/english/recall