The court in New South Wales was established by letters patent dated 2 April 1787 issued by the reigning monarch of England, King George III. These letters authorized the Lords Commissioners of the Admiralty to constitute and appoint a Vice Admiral for the colony, as well as a Judge and any other officers needed for the court to function in the new colony that was soon to be established. The Admirals had authority to appoint vice-admirals and judges in any existing colony. However, as the colony of New South Wales was not yet established, the Admiralty obtained additional letters patent to ensure that there was no legal defect in the constitution of the court. Those further letters patent authorized the Admiralty to make appointments in the new colony.
On 30 April 1787, the High Court of Admiralty issued those letters patent which appointed the first Governor of New South Wales Arthur Phillip as Vice Admiral. Further letters patent were also issued to Robert Ross who was appointed as the first judge of the court.
Arthur Phillip, first Vice-Admiral of New South Wales
Their commissions gave them power to deal with all civil and maritime causes according to the maritime laws and customs which prevailed in what used to be called the High Court of Admiralty in the United Kingdom. At the time of establishment, this included commercial disputes involving ships, seamen's wages, collisions, and salvage. This is what is commonly called an Admiralty Court's “Instance Jurisdiction.” 
Whilst the British admiralty court had jurisdiction over criminal offenses committed upon the high seas, the jurisdiction of the court was rarely invoked. The civil law was well suited to dealing with commercial transactions. However, it could not cope adequately with criminal offenses. The court needed to rely upon the old Roman civil law to establish any breaches. Former Chief Justice Frederick Jordan noted that criminal cases often fell through because sailors weren’t available to give evidence (whether by malice or design). A sentence of death could only not be imposed unless two witnesses could be produced. To deal with this problem, the British Parliament passed the Piracy Act 1698 (UK). This enabled the Crown to appoint seven commissioners to try offenses of piracy under that Act. Whilst that latter court was often called a vice-admiralty court, Australian legal historian John Bennett has shown that that court should not be confused with the present court. The latter court was legally distinct as it was constituted under a separate letters patent dated 12 May 1787 as the Court of Vice-Admiralty and it was constituted by commissioners rather than a judge.
The court sat as a Prize Court, although Bennett points out that there are no records of a prize commission being granted. The first sitting in Prize was in May 1799 when Captain Henry Waterhouse RN ordered the Spanish vessel Nostra Senora de Bethlehem .condemned as a prize of war. Other Spanish vessels condemned during this time were the El Plumier, Euphemia and the Anna Josepha
In 1810 Judge Advocate Ellis Bent questioned the jurisdiction of the court to consider proceedings in prize. As a result, the Admiralty issued warrants and documents to Bent in June 1812 to authorize the court to consider prize, but subsequently revoked Bent's authority in October 1813. As a result, The Eringapatam was unable to be dealt with in New South Wales in 1814 when it was brought into port