Is "to sport ivory" actually forgotten English?

Solution 1:

J.S. Farmer & W.E. Henley, Slang and Its Analogues Past and Present, volume 6 (1903) points out that "sport ivory" was part of a brief eruption of expressions of the form "sport X" (where sport was used as a verb and X was any of a number of nouns or phrases) that began in the early to middle 1780s. Here is Farmer & Henley's entry for the verb sport as a slang term:

[Sport] Verb. (old.)—Generic for display : 'the word was in great vogue ... in 1783 and 1784' (GROSE); now-a-days still general, but spec. a public school and university usage. Thus TO SPORT (or BAULK) a report = to publish far and wide; TO SPORT (= drive) A GIG; TO SORT (= wear) NEW TOGS; TO SPORT IVORY = to grin; TO SPORT (= exhibit) TEMPER; TO SPORT OAK (TIMBER, or TO SPORT IN) = to deny oneself to callers by closing an outer door ... TO SPORT OFF = to do with ease; TO SPORT (= provide) A DINNER; TO SPORT LITERATURE = to write a book; TO SPORT (= spend) MONEY, ONE'S SALARY, &c.; TO SPORT (= express) AN OPINION; ... TO SPORT SILK (racing) = to ride a race; TO SPORT (= indulge or engage in) SMOKING, WALKING, &c. Whence (Winchester) A SPORTING ACTION = an affected manner, gesture or gait, or a betrayal of emotion.

In the context of the geyser of to sport expressions that emerged during and after the great vogue, "to sport ivory" seems less a striking turn of phrase than just another sported-up expression.

The quotation from Francis Grose appears in Grose's A Classical Dictionary of the Vulgar Tongue, second edition (1788):

TO SPORT. To exhibit : as, Jack Jehu sported a new gig yesterday; I shall sport a new suit next week. To sport or flash one's ivory ; to shew one's teeth. To sport timber ; to keep one's outside door shut ; this term is used in the inns of court to signify denying one's self. N. B. The word sport was in great vogue ann. 1783 and 1784.

I see no reason to doubt the specificity of the 1783 and 1784 dating by Grose, given that his book recording the phenomenon appeared only four or five years later.

The first edition of A Classical Dictionary of the Vulgar Tongue (1785), in contrast, has no entry for "to sport"—presumably because Grose had not had time to record the ongoing vogue. But the alternative expression "to flash ivory" receives full attention in the earlier book:

FLASH, a periwig ; rum flash, a fine long wig ; queer flash, a miserable weatherbeaten caxon ; flash also means to show ostentatiously ; to flash one's ivory, to laugh and shew one's teeth ; don't flash your ivory but shut your potatoe trap and keep your guts warm, the devil loves hot tripes.

It thus appears that ivory for "human teeth" was already well established during the flash vogue preceding the sport vogue of 1783–1784. So when the latter mania took hold, coining "to sport ivory" must have been as easy and obvious as falling off a log.

Solution 2:

As a verb, sport is defined (in Google) as:

wear or display (a distinctive or noticeable item).

"he was sporting a huge handlebar mustache"

synonyms: wear, have on, dress in; display, exhibit, show off, flourish, parade, flaunt

"he sported a beard"

Thus, "sport ivory" is to show off your teeth with a wide smile.