The call comes after the death of millionaire stockbroker turned IRA gunrunner Mike Logan, who had agreed to testify against one of the organisation’s most senior commanders.
Mr Logan alleged that in 1995 - a year after the first IRA ceasefire- senior Belfast republican Sean ‘Spike’ Murray asked him to smuggle weapons into Northern Ireland.
Crucially, the gun-running is alleged to have continued after the Good Friday Agreement.
Mr Murray, who is now a key Sinn Fein representative, has continually denied any involvement in operation.
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Detectives had wanted to fly Mr Logan to Northern Ireland to give evidence, but the 57-year-old passed away suddenly in his sleep in Florida last Saturday.
Calls have now been made for the PSNI to clarify the implications for the case in the wake of Mr Logan’s death.
North Antrim MLA Mr Allister told the News Letter: “Regardless of the passing of Mr Logan it is imperative that the PSNI exhaust every avenue to bring those involved in the Florida gun-running to justice.
“The PSNI need to tell us what efforts they made to interview Logan over the past number of years.
“One suspects that political expediency has a great deal to do when it comes to explaining the lack of progress in this case after so many years.”
Ulster Unionist MLA Ross Hussey has said it is a matter of “real regret” that Mr Logan’s evidence as to who he sent hundreds of weapons to will not now be heard in court.
He added: “Mike Logan claimed to have shipped over 200 handguns and other weapons to the Provisional IRA from America over a five-year period, which began after the IRA ceasefire and continued even after the Belfast Agreement.
“Having been a regular visitor to Northern Ireland since the early 1980s, he knew exactly what he was doing and what the deadly consequences of his actions would be.
“Indeed, weapons he supplied are believed to have been used in the murder of two Police officers in Lurgan in 1997.
“It is a matter of real regret that having agreed to give evidence, Mike Logan will now not be able to appear in court.”
Victims’ rights campaigner Ken Funston, whose brother was murdered by the IRA, added: ““This case has been buried for the past two years. I would hope that the case can still be taken forward with Mr Logan, but I would be surprised if it ever goes to court.
“This is yet another legacy case which is politically expedient to file away and forget about.”
A PSNI spokesperson told the News Letter: “It would be inappropriate to comment on an ongoing investigation.”