"with urgent speed, with all possible haste," 1590s, from a noun (1530s) meaning "great speed," usually said to be from "post haste," an instruction formerly written on letters (attested from 1530s), from post (adv.) + haste (n.). The phrase originated in the old system of relaying messages by post horses (see post (n.3)); the verb post "to ride or travel with great speed" is recorded from 1550s.
send it to me post-haste
posteriority
posterity
postern
post-glacial
post-graduate
post-haste
post-hole
post-horse
posthumous
postillon
post-impressionism