John Phillip Harrington, 62, is serving a 4½ year sentence for attempting to possess and trafficking a marketable quantity of cocaine. He will be eligible for parole in May 2016.

But Commonwealth prosecutors have appealed the sentence to the ACT Court of Appeal on the grounds it was manifestly inadequate.

Harrington was arrested in July 2011 after police busted him with more than 258 grams of cocaine - worth about $114,000 - following a trip to the United States.

The drug was intercepted by Customs before police substituted it for an inert substance and followed the trail to Harrington.

A raid of Harrington's Griffith home uncovered 24 grams of cocaine and other drug paraphernalia, including scales and zip-lock bags.

But Harrington claimed he had only been a small stakeholder in the criminal enterprise and intended to use his 15 per cent to fuel his $1200-a-day drug habit.

Justice John Burns rejected the claim, saying the offender had taken too many risks to be such a low-level player.

The Crown sought to appeal the sentence, but filed papers a day past the 28-day expiration period.

The error forced the prosecution to apply for leave to appeal the decision and the matter came before Chief Justice Helen Murrell in the ACT Supreme Court.

The Crown revealed the appeal had been filed a day late after an administrative error meant the date was miscalculated.

The court heard the prosecution had taken issue with Justice Burns' discount for Harrington's guilty plea, the amount of concurrency in calculating the total sentence, and the leniency afforded, considering the offender's criminal history.

But Harrington's lawyer, John Purnell, SC, opposed the application for leave to appeal, on the grounds it would cause his client prejudice, the Crown had not proven special circumstances, and it had not correctly followed court procedure rules in lodging the papers.

Mr Purnell also argued the case law submitted by the Crown to support its bid did not reveal any appealable error.

Chief Justice Murrell granted leave on the grounds that the prosecution had adequately explained the one-day delay, the delay had not caused prejudice, and the case had some merit.

The matter will reappear at a later date.