Here is a list of NSW Governors from 1788 to 1855.... the list is not complete.... we will add more later. Perhaps you can find out what were the years they governed.
List of Governors of New South Wales
Captain (later Vice-Admiral) Arthur Phillip,
Captain John Hunter,
Captain Phillip Gidley King,
Captain (later Vice-Admiral) William Bligh,
Colonel (later Major-General) Lachlan Macquarie
Major-General Sir Thomas Brisbane
Major-General (later General and Sir) Ralph Darling
Lieutenant-General (later General) Sir Richard Bourke,
Lieutenant-Colonel Sir George Gipps
Sir Charles Augustus Fitzroy
List of Governors of New South Wales
Captain (later Vice-Admiral) Arthur Phillip,
Captain John Hunter,
Captain Phillip Gidley King,
Captain (later Vice-Admiral) William Bligh,
Colonel (later Major-General) Lachlan Macquarie
Major-General Sir Thomas Brisbane
Major-General (later General and Sir) Ralph Darling
Lieutenant-General (later General) Sir Richard Bourke,
Lieutenant-Colonel Sir George Gipps
Sir Charles Augustus Fitzroy