hierophant

More precisely: phan- is "show, reveal" in Greek. To it was attached an agent ending -tês (as in the ancestors of 'athlete', 'Cypriot'), so phantês "revealer". Add to this hier- "sacred" and the connecting vowel -o- between consonants, and we get hierophantês "revealer of the sacred", first declension masculine.

In Latin the corresponding ending is -a (as in nauta, agricola), so it got borrowed into Latin as hierophanta. Here normal phonetic processes accumulate to lose the final -a and change the other sounds to their modern English values.

The Greek verb meaning "show" is listed in dictionaries under a citation form—either present indicative phainô "I show" or infinitive phainein "show". This latter consists of the root phan-, a verb class formative (I think) -j-, and the infinitive ending -ein. In early Greek phanj- changed to phain-. So the phant- doesn't come from this; what they share is rather the basic root phan-. It may seem pedantic to write all this out, but I increasingly think the alternative is misleading: to suggest that -phant somehow comes phonetically from phainein.

A prophet; from Greek: 'hiera' holy things 'phanein' to bring to light.