molesworth postcode tasst Home ›› Postcode Finder ›› TASST ›› Molesworth Molesworth local listingsThe suburb of Molesworth is located in TAS and has a postcode of 7140. Free molesworth business listing! 1Molesworth Primary School540 Molesworth Rd 03 62612091 View more business listings in molesworth Search and find other Postcodes in Tasmania or widen the search to Postcodes in Australia.