He was appointed by letters patent of 15 June 1743, issued by Lionel Sackville, 1st Duke of Dorset, Lord Lieutenant of Ireland.
During his time in office he drew plans for barracks at Charles Fort and for the Bedford Tower range at Dublin Castle.
[3] During the 1750s, attempts were made by John Rochfort, MP for Mullingar, to recoup the losses caused, through the introduction of several unsuccessful bills intended "To oblige Arthur Jones Nevill, esquire, late engineer and surveyor-general, at his own expense, and without any further charge to the public, to make good the defects in the several barracks, built, re-built and repaired under his direction, and to complete the same in the most effectual manner, according to the several contracts entered into for that purpose.
When the house was demolished in 1912 the ceiling stucco work was transferred to the state apartments in Dublin Castle.
He introduced a number of bills, including proposals "For the further encouragement of planting timber trees" (1765) and "For the better regulating of buildings in the city of Dublin, the liberties and suburbs thereof" (1769).