Home Postcode finder TAS Barrington Barrington postcode TAS Barrington is a locality in Tasmania covered by postcode 7306. Postcode 7306 State or territory Tasmania (TAS) Region Tasmania Add a free Barrington business listing Be the first listing in Barrington Common questionsWhat is the postcode for Barrington?Barrington, TAS has the postcode 7306.What state is Barrington in?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 Barrington. Browse other postcodes in Tasmania, or widen the search to every Australian postcode.