顧問は学長を推戴し、本会の重要事項に関し諮問に応じる。

、。

The advisor is appointed from among presidents emeritus and responds to inquiries on important matters of this association.

Literal

Advisor [topic-は] president [object-を] reverently-install-[ren'yōkei-し], this-association [attributive-の] important matters [regarding-に関し] inquiries [to-に] respond-[polite-ます].

Highly formal organizational/bylaws language. 推戴 ('to reverently install, to nominate with reverence') is a rare formal kango — used for installing someone as a figurehead, usually an elder or elder statesman. 諮問 ('formal inquiry, consultation by a higher authority') is also formal. ~に応じる ('respond to X'). ~に関し uses the ren'yōkei stem of 関する instead of the attributive 関する — formal written style.