The bitter battle between Alex Turnbull and his father’s former business partner, Russel Pillemer, is set to continue, with a firm part-owned by the son of the former prime minister seeking to have a ruling against it thrown out.

In September last year, Judge Kate Williams dismissed allegations that Mr Pillemer misled the younger Mr Turnbull. He had sued Pillemer Pty Limited through a company called Maurtray, which he owns with his sister, Daisy Turnbull.