Consularis

Consularis is a Latin adjective indicating something pertaining to the consular office. In Ancient Rome it was a title given to those senators who held consular rank, i.e. who had served as consuls or who had received the rank as a special honour. In Late Antiquity, the title became also a gubernatorial rank for provincial governors.

In the Roman Republic, the term [vir] consularis (rendered in Greek ὑπατικός, hypatikos) as originally designated any senator who had served as consul. The distinction was accompanied by specific privileges and honours, and was a necessary qualification for a number of magistracies: the posts of dictator and his deputy, the magister equitum (although some cases seem to refute that), the post of censor as well as the governance of certain provinces as proconsuls. The distinction was attached to their wives as well (consularis femina, in Greek ὑπατική or ὑπάτισσα). The status of a consularis could be gained without holding the consulship, either through the adlectio inter consulares or through the award of the consular insignia (ornamenta/insignia consularia), but this was done only twice under the late Republic, and only became common practice in the Empire.

Under the Empire, a number of senior magistracies were created for consulares:

Already in Republican times, certain provinces were reserved for ex-consuls. This tradition carried into the Empire following the division of the provinces into Imperial and Senatorial in 27 BC. Of the latter, two were specifically reserved for consulares, the proconsular provinces of Asia and Africa proconsularis.Consulares could also hold office in Imperial provinces as the Emperor's delegates (legatus Augusti pro praetore), alongside senators who had not advanced beyond praetor rank or equestrian governors, who were styled procuratores. There was no fixed system of appointment for the Imperial provinces, but those where more than one legion was garrisoned usually received a governor of consular rank.

...
Wikipedia