Bithynia et Pontus
Syme infers that Quadratus served as proconsular legate in Bithynia et Pontus from 80-81. Quadratus was appointed governor of the public province of Crete and Cyrenaica in 84/85. He is mentioned again in the "Acta Arvalia" from January 86 to May 89, indicating he was residing at Rome during that time. In the gap after May 89, he served the emperor as governor of Lycia et Pamphylia from the year 89 to 93