Brushtail and ringtail possums are protected in Victoria, which decides how this job runs. A possum cannot be trapped and dumped somewhere else. It goes back on the same property, within 50 metres of where it was caught, after dusk that night. Moving one is both against the rules and fatal for the animal, since it lands in another possum's territory.
Exclusion is the part that works. Find the entry, usually a broken tile, an eaves gap or the join where a veranda roof meets the wall, wait until it has gone out for the night, seal it, and put up a nest box so it has somewhere else to sleep. The older weatherboards and brick veneers through Belmont and Highton with deep eaves are the regular offenders. Thumping overhead after dark is what people ring about.