Mdtryhht

Which is correct: The Saint Poetic Tradition or The Saintly-Poetic Tradition or the Saint-Poetic Tradition?

I want to write about the tradition of poets who were also saints. Which of the above is correct?

It depends.

If you are writing about the traditions of a group of people called the 'Saint-Poets' or 'Saint Poets' (perhaps these people or these people?) then it's normal to make the adjective that describes them as close to the noun as possible. In that case just as poets have a poetic tradition, Saint-Poets have a Saint-Poetic tradition. I would probably keep the hyphen, even if it isn't present in the noun. You might also talk about the 'Saint Poet tradition'. Using strings of nouns where one noun modifies the other is perfectly normal in English. This construction is frequently used for the similar phrase "warrior monk tradition".

If 'Saint Poet' isn't a recognized term, then you are talking about a tradition that has attributes both of poetry and saintliness. In that case use the adjectival form of both words. Call it the 'saintly poetic tradition'. No need for the hyphen in this case.

If you're writing about poets who were formal saints, "the saint-poet tradition" would express that best. The compound modifier "saint-poet" establishes that there is such a being.

However, if you're writing about poets who were generally saintly,
"the saintly-poet tradition" would best express that. Here you need the hyphenated compound modifier to distinguish the idea from a poets tradition that was in itself saintly.

A compound modifier is a sequence of modifiers of a noun that function as a single unit. It consists of two or more words (adjectives, gerunds, or nouns) of which the left-hand component modifies the right-hand one, as in "the dark-green dress": dark modifies the green that modifies dress. https://en.wikipedia.org/wiki/English_compound#Compound_nouns