The Collaborative International Dictionary of English v.0.48:

Archiepiscopacy \Ar`chi*e*pis"co*pa*cy\, n. [Pref. archi- +
   episcopacy.]
   1. That form of episcopacy in which the chief power is in the
      hands of archbishops.
      [1913 Webster]

   2. The state or dignity of an archbishop.
      [1913 Webster]