Brushtail and ringtail possums are protected in Victoria, and that changes what is allowed. A possum cannot be trapped and dumped in a park across town. It has to be let go on the same property, within 50 metres of where it was caught, after dusk that same night. Moving one somewhere else is both against the rules and a death sentence for the animal, because it lands in another possum's territory with no shelter and no way back.
What actually solves it is exclusion. We find the entry point, usually a broken tile, a gap at the eaves or the join where a veranda roof meets the wall, wait until the possum has gone out for the night, then seal it and put up a nest box so it has somewhere else to sleep. Older homes through Newtown, Drumcondra and Manifold Heights with deep eaves and cast-iron veranda roofs are the regular offenders. Thumping overhead after dark, scratching, and a smell coming through the ceiling are what people ring about.