In a manner relating to or characteristic of a council or councils.
Conciliar + -ly, the standard adverbial suffix. Simply transforms the adjective conciliar into an adverb describing how something happens in relation to councils.
A perfectly logical word formation, but you'll almost never encounter it in actual use—it's the kind of word that exists because English grammar allows it, even if nobody has needed to say it since about 1642.
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