The headword is third person singular, future indicative active, of the verb κατέχω (for which see also kappa 1001, kappa 1002, kappa 1026, kappa 1027); evidently quoted from somwhere.
Same entry in Lexica Segueriana s.v. καθέξει , Photius s.v. καθέξει and Zonaras s.v. καθέξει .
NB: the headword could have been the dative singular of the related feminine noun καθέξις (see Hesychius s.v. ἐν καθέξει ), but is not glossed thus.