A NEW public estate with 400 rental and home ownership scheme units will be built on Cheung Chau for $170 million. The complex will house 1,500 island residents who will be affected by clearance on the island. A Housing Authority spokesman said the estate would provide housing for people living in poor conditions on Cheung Chau and those qualified under the ordinary home ownership scheme criteria. The spokesman said three Harmony ''rural-style'' blocks would be built. ''The rural rental units and home ownership scheme flats are designed to accommodate residents affected by the clearance of Cheung Chau Old Town stage two and three, and Cheung Chau development package six, stage two. ''The project will also provide accommodation for those who are living in poor conditions in Cheung Chau.'' The 304 rental and 100 home ownership scheme flats will be supported by a store and a day care centre for the elderly. The project, with site work due to start in August this year, is expected to be completed by April 1988 at an estimated cost of $170 million. Construction of Cheung Chau's second public estate will start in August and be completed by August 1998. The Housing Authority's building committee has also endorsed the proposed client briefs, concept plans and redevelopment projects for Sau Mau Ping and Kwai Chung estates, Wang Tau Hom phase two and Cheung Chau second rural public housing estate. The Housing Department spokesman said the project would be carried out in 13 phases, with phases one, three, five, seven, eight and nine being rental estates; phases two, four, six and 13 going as home ownership scheme flats and phases 10, 11 and 12 designated for community facilities. ''Major commercial, community and transport facilities are grouped together at the centre of the project for the convenience of residents and to enhance its commercial viability. ''Phase one construction is underway, while phases two to 13 will be carried [between] 1994 and 2005.'' The Kwai Chung estate redevelopment plan has been divided into six phases. Phase one, which features three rental blocks, is due for completion in 1997.