He was sentenced last month to 13 years over the murder of Lapan Nason in 2015.
Today the Supreme Court allowed an application asking the court to appeal his sentence, which was handed down on August 21.
He was previously allowed to appeal against his conviction, dated May 29.
These two appeals will be joined and heard at the same time. The joined appeal will be set at a later date.
Justice Stephen Kassman, in granting leave to hear the appeal, was satisfied the ground proposed had merits.
Among the grounds presented by his lawyers was that the trial judge erred when he failed to address the mitigating circumstances or excuses of the offence as a whole.
Other grounds include the trial judge making comments on the frequency of manslaughter cases in the country without the state presenting any materials before it during submissions on sentence.
Parker was found guilty on May 29 for unlawfully assaulting Lapan Nason on June 6, 2015, that led to his death two days later.
He was convicted for manslaughter, the lesser homicide charge after he stood trial for the charge of wilful murder in the Waigani National Court.
He was sentenced on August 21 to 13 years in prison by Deputy Chief Justice Sir Gibbs Salika.