George Askwith was called to the bar in 1886 and became a member of the Inner Temple. There is no record of his reasons for taking up law, but it was one of the few options available to promising young men. He was the most academically gifted of the five Askwith brothers and the only one in the family to go to university; William, John and Henry, like their father, went into the army, and Charles chose the navy.

After leaving Oxford in 1884, according to the Marlborough College Register, in 1885 Askwith was appointed secretary to General Sir Peter Scratchley and took part in the expedition for the annexation of New Guinea in 1885–1886. Scratchley was appointed Her Majesty's Special Commissioner for the Protected Territory in New Guinea on September 1884 and proposed to set up some coastal stations as centres of government, but his position was precarious. At this time Australia had just extended its control over the Northern Territory and Queensland, and was very concerned that the eastern half of this large island – Germany had already taken possession of the western part – which was so close to their northern shores should be occupied by a friendly power. The growth of French and German influence in the Pacific and the establishment of a French penal settlement in New Caledonia created considerable alarm in Australia about the possibility of a country lying close to their shores passing into possession of a foreign power.