Definition of "rare"

Plant breeding is always a numbers game. […] The wild species we use are rich in genetic variation, and individual plants are highly heterozygous and do not breed true. In addition, we are looking for rare alleles, so the more plants we try, the better.

2013 May-June, David Van Tassel, Lee DeHaan, “Wild Plants to the Rescue”, in American Scientist, volume 101, number 3

While many material components in Andromeda are familiar, we have also discovered rarer and more valuable materials; attributable to exposure to the Scourge, or mysterious alien technology.

2017, BioWare, Mass Effect: Andromeda (Science Fiction), Redwood City: Electronic Arts, PC, scene: Technology: Augmentations Codex entry

Sees her reflection in a butcher shop. / She finds it all quite rare / That her meat's all vanity fair.

1981, Chris Difford (lyrics), Glenn Tilbrook (vocal), "Vanity Fair" (song)

Most of the time, you do this by trading low-valued rares for more valuable ones or trading uncommons for rares. Other times it's trading cards that are in print for ones that are out of print, or low-value rares for good uncommons.

1995, George Baxter, Larry W. Smith, Mastering Magic Cards, page 116

Then Curds and Cream, the Flow'r of Country Fare, / And new-laid Eggs, which Baucis’ buſie Care / Turn’d by a gentle Fire, and roaſted rare.

1717, John Dryden, “Book VIII. [The Story of Baucis and Philemon.]”, in Ovid’s Metamorphoses in Fifteen Books. […], London: […] Jacob Tonson, […], page 285

Frank pretended to rare back as if bedazzled, shielding his eyes with a forearm.

2006, Thomas Pynchon, Against the Day, Vintage, published 2007, page 328

Here I have to say that I was walking along dark-hearted, my nose out of joint about Audie's notice of her, for just as quickly as my feelings kindled, my old envy rared.

2013, Janet Peery, What the Thunder Said: A Novella and Stories

The men, that sway / In work of those tools that so fit our state, / Are rude mechanicals, that rare and late / Work in the market-place;

1614–1615, Homer, “The Sixth Book of Homer’s Odysseys”, in Geo[rge] Chapman, transl., Homer’s Odysses. […], London: […] Rich[ard] Field [and William Jaggard], for Nathaniell Butter, published 1615; republished in The Odysseys of Homer, […], volume I, London: John Russell Smith, […], 1857, page 147, lines 420–423