He entered Colonial Office in 1900 as a second-class clerk, eventually serving as acting first class clerk from 1907 to 1910, when he became a permanent 1st class clerk. In that same year, Stubbs was sent on a special mission to Malay Peninsula and Hong Kong. He was a member of West African Lands Committee in 1912, and became a colonial secretary of Ceylon in from 1913 to 1919.
Governor of Hong Kong
He was appointed Hong Kong Governor in 1919, a position he served until 1925. During Stubbs' tenure, strikes were frequent, thus harming the Hong Kong economy in the process. In 1922, seamen went on strike in Hong Kong. Stubbs engaged in cordial talks with Sun Yat-sen and his supporters in Hong Kong prior to Sun's triumphal return to Canton in February 1923. There followed, in 1925, the general strike that involved workers in Hong Kong and Canton, China. The strikers demanded the annulment of the "unequal treaties". The strikers also demanded better treatment of Chinese labourers on Hong Kong. At first, Stubbs tried to suppress the strikers with legal and forceful means, but the efforts backfired, and caused an exodus of more than 100,000 Chinese labourers to China. Both Stubbs and his Colonial Secretary Claud Severn retired in 1925, having failed to quell the disorder and leaving behind a seriously damaged Hong Kong economy. British Consul General in Canton James Jamieson criticised their leadership, seeing them as out of touch and out of date, unable to converse in Chinese and ignorant of republican China. Stubbs received an M.A. degree during his tenure, in 1920.
After his stormy tenure as Governor of Hong Kong, Stubbs was made Captain-General and Governor-in-Chief of Jamaica a year later, in 1926. He would hold this position until 1932, when he was appointed Governor and Commander-in-Chief of Cyprus. He would serve in this position until 1933.
Governorship of Ceylon
In 1933 Stubbs was appointed to his last position in the Colonial Service: Governor and Commander-in-Chief of Ceylon.
Bracegirdle affair
In 1937, he was prevailed upon by the White planters to become involved in an illegal attempt to deport Mark Anthony Bracegirdle, an Australian planter who had gone over to the side of the workers and joined the Lanka Sama Samaja Party. Bracegirdle was served with the order of deportation on 22 April and given 48 hours to leave, but he defied the order, going into hiding instead. The Colonial Government began a man-hunt, but was unsuccessful. The LSSP started a campaign to defend him. At that year's May Day rally at Price Park, Colombo placards declaring 'We want Bracegirdle – Deport Stubbs' were displayed, and a resolution was passed condemning Stubbs, demanding his removal and the withdrawal of the deportation order. On 5 May, in the State Council, the LSSP members Dr N.M. Perera and Philip Gunawardena moved a vote of censure on the Governor for having ordered the deportation of Bracegirdle without the advice of the acting Home Minister. Even the Board of Ministers had started feeling the heat of public opinion and the vote was passed by 34 votes to 7. On the same day there was a 50,000-strong rally at Galle Face Green, which was addressed by Dr N.M. Perera, Philip Gunawardena, and S.W.R.D. Bandaranaike, condemning Stubbs. Bracegirdle made a dramatic appearance on the platform at this rally, but the police were powerless to arrest him. They managed to arrest him a couple of days later, but a writ of habeas corpus was served and the case was called before a bench of three Supreme Court judges presided over by Chief Justice Sir Sidney Abrahams. The brilliant H.V. Perera, the county's leading civil lawyer, volunteered his services free on behalf of Bracegirdle; he was made a King's Counsel on the day that Bracegirdle appeared in court. On 18 May order was made that he could not be deported for exercising his right to free speech, and Bracegirdle was a free man. Stubbs retired shortly afterwards.