A part-time member of the UDR, the 39-year-old was fatally shot in Strabane, Co Tyrone in June 1982.
He was targeted as he got into his car to drive home for lunch. He had worked at the same drapery store for 25 years.
No-one has ever been brought to justice.
His niece Shelley Gilfillan has been campaigning for a new investigation into the murder.
On Monday, she went to the police headquarters in east Belfast to meet Assistant Chief Constable Drew Harris. Also present were senior figures from the DUP.
Shelley told UTV: "I was told that the case is going to be re-opened and re-investigated. That is brilliant news.
"It was a very difficult meeting today, very emotional but I am glad to see that the case is now going to be re-opened.
"It is the right for us victims to see justice, see justice for our loved ones that are no longer here. I think they deserve that."
She admitted that she now feels more reassured that justice will finally be done.
"Absolutely, I absolutely feel a lot more confident now that things are going to be looked into and yes, I've a lot more confidence out there that justice [will be done], we're going to get there."
For Shelley, this new investigation is a major step forward. Decades may have passed but she remains confident the evidence is still there.
Finding it will be not easy job for the police.
Jonathan Craig, DUP MLA and Policing Board member, said: "They are going to do as full investigation of all sources, of forensics within the PSNI, they seem to be scattered right across the organisation, they are going to try and find the forensic evidence that actually existed 30 odd years ago and that was evidence which would have led to a conviction."
The meeting was arranged after the so-called on-the-run controversy, sparked by the collapse of the case against Republican John Downey in February.
The case against the Co Donegal man accused of carrying out the 1982 Hyde Park bombing in London collapsed, after being thrown out by a judge at the Old Bailey.
Downey, 62, had been charged with the murders of four soldiers after his arrest at Gatwick Airport last year. He strenuously denies the charges that had been put to him.
He was detained because his name was on the UK's most wanted list - but in 2007, despite the outstanding warrant, he had been granted an immunity deal.
At the Old Bailey, Judge Mr Justice Sweeney branded the blunder by the PSNI a "catastrophic error".
It is understood that 187 such immunity letters were issued to terror suspects.
Shelley strongly believes one of her uncle's killers may have also received what has been dubbed a comfort letter.
There have already been a number of investigations into the murder of Hugh 'Lexie' Cummings - first the original police investigation, then one by the Historical Enquiries Team (HET), and another by the so-called On The Run review team which was carried out in 2003.
According to the Historical Inquiries Team, the review was conducted after a suspect - who is now a Sinn Féin councillor in the Republic - was included "on a list of OTR's supplied by Sinn Fein to H.M Government"
However, the HET said that after this review - requested by the Director of Public Prosecutions - "the DPP rescinded the direction of December 13, 1982, to prosecute" the republican.