The headword appears to be an aorist of peristh/kw, a late present formed from the perfect of perii/sthmi (see LSJ s.v. sth/kw, web address 1). The same entry occurs in the Synagoge, Lexica Segueriana 338.19, and Photius pi681, where Theodoridis obelizes the transmitted headword and supports Dindorf's proposed emendation to perie/steican. Cobet, followed by Naber, argues for perie/tican, but the glossing would not fit; cf. under sigma 75. In fact the entry seems likely to have been generated by Acts 25.7; there the accepted text has perie/sthsan (web address 2), but perie/sthcan could be a variant reading.
See also pi 1136, pi 1138, pi 1161, pi 1162, pi 1163, pi 1164.