[5] It is possible his relative Marcus Durmius helped Quadratus at the beginning of his senatorial career by facilitating his entrance into the decemviri stlitibus iudicandis, one of the four boards that comprised the vigintiviri, a minor magistracy that was a required first step to enter the Senate.
[7][8] Quadratus could have expected to acceded to the consulship upon in due course, but his only known office for many years after conclusion of his tenure as curator was proconsular governor of Cyprus, a modest public province.
[1] Quadratus is next attested as governor of the imperial province of Lusitania in 37 AD, administering the oath of allegiance to the new emperor on Tiberius' death.
The previous governor, Fulcinius Trio, returned to Rome before 1 July 31 when he began his tenure as suffect consul; normally governors served for three years at a time, and another man may have been in office between him and Quadratus, but at this point in his reign Tiberius often prolonged the time senators were assigned to imperial provinces; it is possible Quadratus was dispatched to distant Lusitania as early as the year 31,[9] and remained there through the reign of Caligula.
He did not remain in Rome long, for he is attested appointed by Claudius as governor in "Illyria"—either the province of Dalmatia or Pannonia.
The procurator of Iudaea, Ventidius Cumanus, was accused of partiality to the Samaritans, who were at variance with the Galileans, and both parties appealed to Quadratus.
In fear of further disturbances, Quadratus hurried to Jerusalem; finding the city peacefully celebrating the Feast of Passover, he returned to Antioch.