All 3 Uses of

pious
in
Hamlet, Prince of Denmark

Breathing like sanctified and pious bawds, The better to beguile.
Scene 1.3 *

pious = highly religious and moral

The first row of the pious chanson will show you more; for look where my abridgment comes.
Scene 2.2

pious = religious

—We are oft to blame in this,— 'tis too much prov'd,—that with devotion's visage And pious action we do sugar o'er The Devil himself.
Scene 3.1 *

pious = appearing highly religious and moral even though it's not true

Definitions:

(1) (pious as in: a good, pious woman)
religious or highly moral
(2) (pious as in: a pious hypocrite)
self-righteous (acting as though one is, or believing one is highly moral when it is not true)
(3) (pious as in: cling to the pious hope)
(describing a hope or wish as) sincere, but highly unlikely
(4) (meaning too rare to warrant focus)
meaning too rare to warrant focus:

Much more rarely, piety can refer to devotion or faithfulness as Proust used it in the book, Swann's Way:

"...but when, as had befallen me, such an anguish possesses one's soul before Love has yet entered into one's life, then it must drift, awaiting Love's coming, vague and free, without precise attachment, at the disposal of one sentiment to-day, of another to-morrow, of filial piety or affection for a comrade."