"The Holy Spirit"
because here it does not describe the spirit, but distinguishes it from the others.
I think (but I am not sure how accurate it is), that in this particular example Holy=Święty goes after noun, and święty=saint goes before.
we had a long conversation about adjectives behind the nouns here https://www.duolingo.com/comment/13508523
I think it's actually idiomatic, probably inherited from the Latin "Spiritus Sanctus"