hitchhiker

A cryptic clue typically breaks into two distinct parts, a definition and some wordplay, both of which lead to the same answer. The definition will be either at the beginning or at the end of the clue, and there is sometimes a connector between the two halves that is some variant of "A is B" or "A leads to B".

Here the breakup is

Cathedral | [to be] | remade, not demolished.

Cathedral = definition
to be = connector
remade, not demolished = wordplay

there are a set of conventions for the wordplay; the one I'm using here is the anagram clue, which has an anagram indicator (typically some word indicating "break", "rearrange" or "construct", or an adjectival phrase like "in turmoil") next to the fodder, a group of words whose letters get anagrammed. here the indicator is "demolished", and the fodder is "remade not", so the wordplay is literally saying "[the letters of] remade not" demolished [i.e. anagrammed].

so now we have something that is two words of (5, 4) letters, defined by "Cathedral" and where the answer is an anagram of "remade not", which makes it unambiguously NOTRE DAME.

The fact that the surface (the clue when read as a normal english fragment) refers to the answer is a bonus; it's rare in actual crosswords but nice when writing topical clues like this.