Moore ran again for re-election to the three-member Redfern Ward in the 14 April 1984 Council Election, and was highly successful, taking first position, outpolling Bill Hartup with a 21% swing against the ALP, and enabling the election of the second candidate on her independent ticket, Sue Willis, ahead of the sitting Labor Alderman Stan Champley. In May 1984, Moore ran for the position of Deputy Lord Mayor after the election, but was defeated by the main right-wing Labor candidate, Stan Ashmore-Smith, when the two Independent Communist Aldermen (Jack Mundey and Brian McGahen) sided with the Labor caucus in the vote. Moore proved a high profile campaigner on heritage preservation and environment conservation, gaining the ire of the Miscellaneous Workers' Union when she confronted a Council worker who was undertaking unsympathetic pruning to trees on a street in Redfern exclaiming "its hard enough for trees to survive city pollution without their being massacred by untrained workmen sent to prune them", and denouncing the Sydney Cricket Ground Trust as "architectural barbarians, insensitive to the traditions of the ground" for approving the demolition of the historic 1909 Sheridan Stand of the Sydney Cricket Ground, which was nonetheless razed in 1986.