A recent episode of television programme Cold Case focused on the new team's investigation, with Detective Senior Sergeant Warwick McKee saying police were now following up fresh information as a result.
This included speaking with a number of suspects and collecting DNA from each of them.
Investigators speaking in the Cold Case episode said they had long viewed one man as the key suspect after visiting his home and having him admit he had experience in bomb-making.
Investigators also found bomb-making ingredients, including safety fuses and a pack of detonators.
They also crucially found a copy of a 1977 newspaper.
Pages from the same edition of the newspaper had been found to have been packed inside the suitcase containing the bomb.
The man's profile as a disgruntled recluse also fitted with the case, investigators said.
Despite all this evidence, police were unable to build a case against the man.
However, in the Cold Case episode, investigators said the man was still alive and they now hoped DNA collected from the bomb site could be matched against that of the man to prove his guilt.
A former marine engineer is now believed to be the chief suspect, according to Stuff.
The new investigation comes after the bombing on March 27, 1984, shocked the nation.
On that Tuesday, Wellington Trades Hall caretaker Ernie Abbott was locking up for the day.
But at 5.19pm he picked up a suitcase, which had been left unattended for several hours.
The movement triggered a bomb and Abbott was killed almost instantly.
Police investigators said they initially believed the blast to be from a gas explosion, unable to comprehend that a bombing attack had been made in New Zealand.
The attack came at a time when former Prime Minister Sir Robert Muldoon was locked in a fight with trade unions over workers' pay.
