"wasp's nest," 1816, from Latin vespa "wasp" (see wasp) on model of apiary. A proper formation would be *vespary.
Entries linking to vespiary
wasp n.
Old English wæps, wæsp "wasp," altered (probably by influence of Latin vespa) from Proto-Germanic *wabis- (source also of Old Saxon waspa, Middle Dutch wespe, Dutch wesp, Old High German wafsa, German Wespe, Danish hveps), from PIE *wopsa-/*wospa- "wasp" (source also of Latin vespa, Lithuanian vapsa, Old Church Slavonic vosa "wasp," Old Irish foich "drone"), perhaps from root *(h)uebh- "weave" (see weave (v.)). If that is the correct derivation, the insect would be so called for the shape of its nest. Of persons with wasp-like tendencies, from c. 1500. Wasp-waist in reference to women's figures is recorded from 1870 (wasp-waisted is from 1775).
apiary n.
1650s, from Latin apiarium "bee-house, beehive," noun use of neuter of apiarius "of bees," from apis "bee," a mystery word unrelated to any similar words in other Indo-European languages. A borrowing from Semitic has been proposed; de Vaan finds it "conceivable." Related: Apiarian (1798).