The Collaborative International Dictionary of English v.0.48:

Incumbency \In*cum"ben*cy\, n.; pl. Incumbencies. [From
   Incumbent.]
   [1913 Webster]
   1. The state of being incumbent; a lying or resting on
      something.
      [1913 Webster]

   2. That which is physically incumbent; that which lies as a
      burden; a weight. --Evelyn.
      [1913 Webster]

   3. That which is morally incumbent, or is imposed, as a rule,
      a duty, obligation, or responsibility. "The incumbencies
      of a family." --Donne.
      [1913 Webster]

   4. The state of holding a benefice; the full possession and
      exercise of any office.
      [1913 Webster]

            These fines are only to be paid to the bishop during
            his incumbency.                       --Swift.
      [1913 Webster]

WordNet (r) 3.0 (2006):

incumbency
    n 1: the term during which some position is held [syn: tenure,
         term of office, incumbency]
    2: a duty that is incumbent upon you
    3: the office of an incumbent