sport (v.)
c.1400, "to take pleasure, to amuse oneself," from Old French desporter, deporter "to divert, amuse, please, play" (see disport). Restricted sense of "amuse oneself by active exercise in open air or taking part in some game" is from late 15c. Meaning "to wear" is from 1778. Related: Sported; sporting.
sport (n.)
early 15c., "pleasant pastime," shortening of disport "activity that offers amusement or relaxation; entertainment, fun" (c.1300), also "a pastime or game; flirtation; pleasure taken in such activity" (late 14c.), from Anglo-French disport, Old French desport, deport "pleasure, enjoyment, delight; solace, consolation; favor, privilege," related to desporter, deporter "to divert, amuse, please, play" (see sport (v.)).

Original sense preserved in phrases such as in sport "in jest" (mid-15c.). Meaning "game involving physical exercise" first recorded 1520s. Sense of "stylish man" is from 1861, American English, probably because they lived by gambling and betting on races. Meaning "good fellow" is attested from 1881 (as in be a sport, 1913). Sport as a familiar form of address to a man is from 1935, Australian English. The sport of kings was originally (1660s) war-making. Other, lost senses of Middle English disport were "consolation, solace; a source of comfort."