This is plate 9 from James Baillie Fraser's 'Views of Calcutta and its Environs'. Fraser (1783-1856) arrived in Calcutta in 1814 and in six years produced these animated sketches of the busy.
He devotes three views in the collection to the Government House, all of them taken along its eastern side. This view "from the north-east," writes Fraser, was "taken from the premises of Johnson and Company in Old Court House Street, shows the north front and the northern wings crowned with the Company's coat-of-arms". He draws the Governor General Lord Hastings "about to set off for a drive, as his carriage and bodyguard await him". The grounds are "surrounded by an iron railing upon a plinth interrupted by four triumphal gateways at both ends of the carriageways running across the north and south facades of the building. Beyond the far gateway of Government House, we can see part of the Treasury building in Council House Street, and the east wall of the Town Hall".
Source: British Library (bl.uk)