Trevor Fleet, 73, died earlier this month, following a hit-and-run in Bega in southern NSW.
It has been four weeks since the incident, but police are yet to find the driver.
Detectives believe the offender remains in the local area and are appealing for public information.
Police are urging a woman they believe reversed into and killed a 73-year-old man following an argument on the NSW South Coast last month to come forward.
Eden man Trevor Fleet was struck by a vehicle on August 31 at 12:16pm at Newtown Road near the intersection of the Princes Highway at Bega.
It is believed that Mr Fleet and a woman had pulled over to the side of the road and had a face-to-face argument before the alleged offender returned to her vehicle and reversed into him.
Mr Fleet fell to the ground, sustained serious injuries and died in hospital the next day.
Four weeks on, NSW Police said they were looking for a woman in her 30s or 40s.
"The offender remains in the community and knows what has occurred," said Detective Inspector Justin Marks.
"I'm hoping the offender has a conscience.
"I'm hoping the offender comes forward and is … given the opportunity to provide her version of events."
NSW Police believe the meeting between the two was not planned.
Detective Marks said Mr Fleet's partner was in their vehicle at the time and is still "traumatised" from the incident.
"Trevor was a husband, a loving parent, a family member and a friend to many," he said.
NSW Police has established Strike Force Dalore to investigate, combing through witness statements, CCTV and submissions via CrimeStoppers.
They are now after the public's help to narrow their search for a Caucasian woman of "solid build", five-and-a-half feet tall, with a round face and hair.
She was wearing navy blue work pants and a dark long-sleeve jumper, and was driving a large silver SUV, believed to be a Holden brand, with NSW black and white number plates and a bull bar.
"Investigators believe that other motorists driving past at the time may have witnessed Mr Fleet being hit by this vehicle," said Detective Marks.
"Unless that person was travelling through Bega to travel south or north, that person had to be in Bega for a reason. So we're assuming that that person is tied to the community.
"No piece of information is too small, and what may seem as insignificant could prove vital to this investigation."