The Collaborative International Dictionary of English v.0.48:
Incumbency \In*cum"ben*cy\, n.; pl. Incumbencies. [From
1. The state of being incumbent; a lying or resting on
2. That which is physically incumbent; that which lies as a
burden; a weight. --Evelyn.
3. That which is morally incumbent, or is imposed, as a rule,
a duty, obligation, or responsibility. "The incumbencies
of a family." --Donne.
4. The state of holding a benefice; the full possession and
exercise of any office.
These fines are only to be paid to the bishop during
his incumbency. --Swift.