Astronomers at the Palomar Observatory have discovered a distant supernova explosion, one that they believe is a type previously unknown to science.
Option Elimination -
(A) that they believe is - The trap here is the wrong flexible modifier constriction and the meaning. In a flexible modifier construction, we have a noun (noun or pronoun) + modifier (relative clause starting with that or ed verbal or ING verbal). Here, if we see carefully, that is not acting as a "relative pronoun." Is it referring to anything? No. It's just a connector. Wrong construction. Moreover, "of a type" is better than "explosion .. a type." Explosion is not a type; it is of a type.
(B) that they believe it to be - the same "that" issue. Moreover, why additional "it" to refer to an explosion when we already have "one."
(C) they believe that it is of - Why additional "it" to refer to explosion when we already have "one."
(D) they believe that is - what is the role of "that"? Is it acting as a relative pronoun? No. There is no noun that it is referring to. Is it a connector? No. There is no noun after "that." Moreover, we want to say an explosion is a type of explosion previously unknown, and not an explosion is an explosion previously unknown.
(E) they believe to be of - Noun clause introduced by a pronoun "one" adding more information about a distant supernova explosion. Moreover, one...of a type is correct.