Brushtail and ringtail possums are protected in Victoria, which decides how this job runs. A possum cannot be trapped and dumped elsewhere. 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 what actually works. Find the entry, usually a broken tile, an eaves gap or the join where a veranda roof meets the wall, wait until the possum has gone out for the night, seal it and put up a nest box. The older beach houses through Queenscliff, Point Lonsdale and Barwon Heads with deep eaves and lean-to roofs are the regular offenders.