Abbatial

The abbatial residence, still existent, has a curious exterior pulpit built into the wall, examples of which are not too frequent in France.

Source: tatoeba (12444390)

a possible abbatial vacancy

Source: wiktionary

Thus the abbatial succession came to be confined to members of the clan of the founder; and although originally the abbots were elected from the "founder's kin," and were distinct from those of the clan who possessed the abbatial lands, yet in process of time ecclesiastical line was merged in the secular, and both were united in one lay official, like the successors of St. Patrick at Armagh, who were the objects of St. Bernard's denunciations

Source: wiktionary