Archibald Acheson 1st Viscount Gosford of Market Hill was educated at Trinity College Dublin University Dublin County Dublin Ireland.
He held the office of Member of Parliament (M.P.) for the University of Dublin [Ireland] between 1741 and 1760.
He succeeded to the title of 6th Baronet Acheson of Market Hill [in Clonekearney] co. Armagh [N.S. 1628] on 8 February 1748/49.
He held the office of Sheriff of County Armagh in 1751.
He held the office of Deputy Governor of County Armagh between 1756 and 1761.
He held the office of Sheriff of County Cavan in 1761.
He held the office of Member of Parliament (M.P.) for County Armagh [Ireland] between 1761 and 1776.
He was invested as a Privy Counsellor (P.C.) [Ireland] on 7 May 1770.
He held the office of Member of Parliament (M.P.) for County Enniskillen [Ireland] in 1776.
He was created 1st Baron Gosford of Market Hill co. Armagh [Ireland] on 20 July 1776.
He was created 1st Viscount Gosford of Market Hill co. Armagh [Ireland] on 20 June 1785.