Source : Webster's Revised Unabridged Dictionary (1913)

Eldership \Eld"er*ship\, n.
   1. The state of being older; seniority. ``Paternity an
      eldership.'' --Sir W. Raleigh.

   2. Office of an elder; collectively, a body of elders.

Source : WordNet®

eldership
     n : the office of elder