All 4 Uses of

incumbent
in
Pride and Prejudice

As to her younger daughters, she could not take upon her to say—she could not positively answer—but she did not know of any prepossession; her eldest daughter, she must just mention—she felt it incumbent on her to hint, was likely to be very soon engaged.†
p. 70.3

It is particularly incumbent on those who never change their opinion, to be secure of judging properly at first.†
p. 92.5 *

Elizabeth, feeling it incumbent on her to relieve him from so unpleasant a situation, now put herself forward to confirm his account, by mentioning her prior knowledge of it from Charlotte herself; and endeavored to put a stop to the exclamations of her mother and sisters by the earnestness of her congratulations to Sir William, in which she was readily joined by Jane, and by making a variety of remarks on the happiness that might be expected from the match, the excellent character of Mr. Collins, and the convenient distance of Hunsford from London.†
p. 124.6

For about three years I heard little of him; but on the decease of the incumbent of the living which had been designed for him, he applied to me again by letter for the presentation.†
p. 195.8

Definitions:

(1) (incumbent as in: the incumbent governor)
the person who currently holds an official position
(2) (incumbent as in: incumbent upon her to)
necessary (for someone) as a duty or responsibility
(3) (meaning too rare to warrant focus)
meaning too rare to warrant focus:

Much more rarely (and generally archaically) "incumbent" can also mean resting, leaning, or bent downward. For example:
- "two incumbent figures, gracefully leaning upon it"
- "the incumbent geological formation"
- "the incumbent load"
- "the bird's incumbent toe"