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

Moby Thesaurus II by Grady Ward, 1.0:

71 Moby Thesaurus words for "incumbency":
   accountability, accountableness, advowson, amenability,
   answerability, answerableness, appointment, bale, benefice, berth,
   billet, burden, burdening, burthen, care of souls, cargo, charge,
   charging, cumber, cumbrance, curacy, cure, deadweight,
   dedication to duty, devotion to duty, drag, duteousness,
   dutifulness, employment, encumbrance, engagement, freight, gig,
   glebe, handicap, incubus, job, lading, liability, living, load,
   loading, millstone, moonlighting, office, opening, oppression,
   overload, overtaxing, overweighting, place, position, post,
   prelacy, pressure, rectory, responsibility, responsibleness,
   saddling, second job, sense of duty, sense of obligation, service,
   situation, station, superincumbency, surcharge, taxing, tenure,
   vacancy, vicarage