Greg's brother Phil played 400 first grade rugby league games in England in the 1980s for St Helens R.F.C.
Their sister Trish married Australian rugby league identity Wayne Bennett, the former national, state and multiple-premiership winning coach.
Veivers also had a spell playing in England for Huddersfield alongside fellow Queenslander and future brother-in-law Wayne Bennett.
Veivers remained true to Queensland and was a mainstay of the side for the next eight years representing on 16 occasions.
He was selected for Australia for the 1975 World Series competition and he played in sides captained by Graeme Langlands, John Brass and Arthur Beetson.