Strike force detectives released an image of a dark coloured 2013 to 2017 Holden Commodore VF SSV V8 sedan, which matches the description of a vehicle they believe is linked to the fatal shooting of the 61-year-old grandmother in June.
Investigators suspect the vehicle is linked to persons involved in the shooting, either directly or through a third party.
It comes after Ms Klimovitch was shot in the chest after she answered her front door on Queen Street just after 8pm on Wednesday, June 9.
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She died at the scene.
One of Ms Klimovitch's three daughters, 31, and infant grandson were inside the home when she was gunned down, but were not injured.
Newcastle police commander Detective Superintendent Wayne Humphrey said he believed it was a targeted attack that took the life of the well-known retired swimming teacher, who was remembered by friends as "absolutely beautiful" and "a warm and loving person".
In a statement to media, Detective Superintendent Humphrey described the incident as "horrendous".
"An innocent person has answered the front door of a home and she's been shot in the chest and killed in the presence of a relative and a child," he said at the time.
"It doesn't get any worse."
Police attended the scene but the shooter had already fled the property by the time they arrived.
The offender is thought to have escaped along Little William Street.
Officers from Newcastle City Police District soon established Strike Force Backhouse to investigate the circumstances surrounding Ms Klimovitch's murder.
As police continue to investigate the death, strike force detectives have released the image of the vehicle to the public in a plea for information.
Investigators are appealing to anyone who may have noticed a vehicle matching this description in and around the area at the time of the homicide to contact Newcastle Police or Crime Stoppers on 1800 333 000.
Anyone who may have information that could assist Strike Force Backhouse investigators, including dashcam or CCTV footage from the time of the offence, is urged to come forward.
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