How can I understand this usage of the conditional?

Question

In the following paragraph, "l'imparfait" is used. But then, "le conditionnel présent" is used.

(From the book Dans le café de la jeunesse perdue of Patrick Modiano, p. 29-30) J'ai serré [...] J'étais [...] Je me tenais [...] Cela me suffisait [....] Je me sentais [...] Le [café] était pour moi un refuge contre tout ce que je prévoyais de la grisaille de la vie. Il y aurait une part de moi-même — la meillure — que je serais contraint, un jour, de laisser là-bas.

At first, I was very confused about the bold part, it didn't sound right to me. Now, I think that it is used like this because it is supposed to refer to the "prévoyais" part.

So, I would translate the last sentence like this: [That] there would be a part of me - the best part - which I would be, one day, forced to leave there.

But I'm still not sure if I understand how exactly it is connected to the second-to-last sentence.

Answer 1

The conditional mood can also be used to express an action due to happen in the future, but seen from a perspective set in the past. It is the "future of the past".

Ex:

Il pense qu'il y aura beaucoup de monde.

If set in the past, the sentence becomes:

Il pensait qu'il y aurait beaucoup de monde.

This is how the verb aurait is used in Modiano's sentence: the narrator made a prediction for something due to happen in the future.