Expire

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late Middle English: from Old French expirer, from Latin exspirare ‘breathe out’, from ex- ‘out’ + spirare ‘breathe’.

wiktionary

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Borrowed from Middle French expirer, from Latin exspīrō, exspīrāre, from ex-(“out”) + spīrō, spīrāre(“breathe, be alive”)

etymonline

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expire (v.)

c. 1400, "to die," from Old French expirer "expire, elapse" (12c.), from Latin expirare/exspirare "breathe out, blow out, exhale; breathe one's last, die," hence, figuratively, "expire, come to an end, cease," from ex "out" (see ex-) + spirare "to breathe" (see spirit (n.)). "Die" is the older sense in English; that of "breathe out" is attested from 1580s. Of laws, patents, treaties, etc., mid-15c. In 17c. also transitive. Related: Expired; expiring.