Both Uses

expedient
in
Common Sense, by Thomas Paine
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That as even the best terms, which we can expect to obtain, can amount to no more than a temporary expedient, or a kind of government by guardianship, which can last no longer than till the colonies come of age, so the general face and state of things, in the interim, will be unsettled and unpromising.†
Chpt 3.

expedient = convenient, speedy, or practical; or an action that is speedy or practical
Expedience and right are different things.†
Chpt 4. *

expedience = convenience, speediness, or practicality

Definitions:

(1) (expedient)
convenient and practical, but sometimes not the best or most moral choice
(2) (meaning too rare to warrant focus)
Much more rarely, expedient can also imply that an action was taken for reasons of self-interest rather than for moral reasons.

In the sense of speedy, the word is less commonly used today than in the past; though it may still be used as in "an expedient end" or "an expedient amount of time," or "We are depending upon your expediency."