The "doubled" preposition "auf A hin" (A stands for a noun that fits as in "auf die Gefahr hin, dass ...") is a bit difficult to explain.
I have looked at duden.de, entry hin, and I think duden.de's attempt to make it understandable ist not worth much for those who learn German.
DWDS, hin, is a bit better, they speak of "Kausalzusammenhang", but I doubt that a learner will be able to handle the preposition "bracket" auf A hin properly with this hint.
I would not say that
Auf die Gefahr hin, dass ich mich wiederhole, möchte ich darauf hinweisen, dass ..."
is a connection of cause.
I think such special prepositions should have an own entry in dictionaries with sufficient examples as
auf die Gefahr hin, auf sein Bitten/Drängen hin, auf diese Anzeichen hin etc.
"auf" alone would not be sufficient in the above examples. I compare these German compound prepositions to English ones of the type on to/onto/unto and others of this type. English has both parts of the preposition before the noun, German puts one part before and the other part after the noun.
There are other double prepositions such as auf A zu, zu A hin, von A her etc.
I don't even know whether there is a standard term for this type of prepositions.