Paul McNally, a 26-year-old father of two, was shot as he left Sean Graham's bookmakers at the junction of Brompton Park and Crumlin Road.
He died in hospital two days later.
Police believe two gunmen opened fire in a random sectarian attack on a group of men, at around 2.40pm on 5 June, 1976.
Mr McNally and another man suffered serious injuries.
A 55-year-old man was arrested by officers from the PSNI Serious Crime Branch in Belfast on Monday, after the inquiry was re-opened when new information was received.
Detective Chief Inspector Justyn Galloway said: "Much has changed over the past 36 years in many aspects of life, in terms of policing, politics, personal outlooks and relationships
"I would appeal to people who spoke with police at the time of the murder to make contact with the new investigation team. I would also ask those who may not have previously spoken to police to contact detectives investigating Paul McNally's murder."
Mr McNally, who worked as a plumber, was married and had a four-year-old daughter and a five-month-old son.
A passing army patrol opened fire on his killers as they fled the scene in a yellow Ford Cortina, which had been hijacked in the Shankill Road area before the attack.
The man who was arrested is being questioned by police in Antrim.
Mr Galloway continued: "I fully appreciate the challenges of renewing an investigation into events which took place more than 36 years ago but I believe there are people in the Ardoyne and elsewhere who can assist.
"I would ask those who have information about Paul's murder to think about what they know, do the right thing and talk to police."