The Collaborative International Dictionary of English v.0.48:

Incumbency \In*cum"ben*cy\, n.; pl. Incumbencies. [From
   Incumbent.]
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   1. The state of being incumbent; a lying or resting on
      something.
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   2. That which is physically incumbent; that which lies as a
      burden; a weight. --Evelyn.
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   3. That which is morally incumbent, or is imposed, as a rule,
      a duty, obligation, or responsibility. "The incumbencies
      of a family." --Donne.
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   4. The state of holding a benefice; the full possession and
      exercise of any office.
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            These fines are only to be paid to the bishop during
            his incumbency.                       --Swift.
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