His first solo exhibition was at the Peter McLeavey Gallery, Wellington, in 1978. He regularly exhibits in Wellington, Auckland, Sydney and Hong Kong and has exhibited work in Los Angeles, Europe, throughout New Zealand and Australia. Aberhart has received a number of Arts Council of New Zealand Awards, a Fulbright Travel Grant (USA, 1988), a Fulbright Research Fellowship (USA, 2010) and a Moet et Chandon Fellowship in France (1994).