This archaic British English word for riding at full gallop has strong associations with the hunting field. Those dictionaries that mention it say it imitates the sound of the hooves of galloping horses, but I can’t help but feel that a better origin lies in the three notes of the huntsman’s horn when rallying the riders, one that is echoed in a hunting song of 1787 by the Irish dramatist John O’Keefe: “With a hey, ho, chivy / Hark forward, hark forward, tantivy”. [chivy or chevy is another old hunting cry.]
A once-common figurative usage was to ride tantivy, to go at something full speed or headlong, of which a late example appears in Australia Felix by Henry Handel Richardson (1917): “He was of a nature to ride tantivy into anything that promised excitement or adventure”.
A century earlier, the ubiquitous Sir Walter Scott had a character say in Peveril of the Peak, published 1824: “There are those amongst us who ride tantivy to Rome, and have already made out half the journey”. This used the word in another sense, of a nickname given to high churchmen and Tories in the years after the Restoration of the monarchy in 1660. It came from a caricature published in 1681 that showed a group of churchmen riding the horse of the Church of England madly towards Rome, that is, turning to Catholicism.