Home Postcode finder TAS Lower Barrington Lower Barrington postcode TAS Lower Barrington is a locality in Tasmania covered by postcode 7306. Postcode 7306 State or territory Tasmania (TAS) Region Tasmania Add a free Lower Barrington business listing Be the first listing in Lower Barrington Common questionsWhat is the postcode for Lower Barrington?Lower Barrington, TAS has the postcode 7306.What state is Lower Barrington in?Lower Barrington is in Tasmania (TAS).Does postcode 7306 cover more than one suburb?Yes. Postcode 7306 covers 20 localities, so the postcode alone does not identify Lower Barrington. Browse other postcodes in Tasmania, or widen the search to every Australian postcode.