This word is acceptable for play in the US & UK dictionaries that are being used in the following games:

• Lexulous
• Wordscraper
• Wordosaur

adj. of or relating to an exarch

"But synods, approaching nearer to the modern signification of a plenary council, are to be recognized in the synodical assemblies of bishops under primatial, exarchal, or patriarchal authority, recorded from the fourth and fifth centuries, and possibly earlier."