c. December - Bishop George Berkeley's economic text The Querist begins publication anonymously in Dublin.
Construction of the Magazine Fort in Phoenix Park, Dublin, begins.
Thomas Carte's An History of the Life of James, Duke of Ormonde begins publication in London.
The first known printed poetry by an Ulster Scots writer (in the Habbie stanza form) is published in a broadsheet in Strabane.
February 27 - Thomas Conway, soldier of fortune (d. c.1800)
July 19 - Garret Wesley, 1st Earl of Mornington, politician and composer (d. 1781)
September 22 - Charles Bingham, 1st Earl of Lucan, politician (d. 1799)
William Blakeney, British Army officer and politician (d. 1804)
Thomas Busby, soldier and innkeeper (d. 1798)
Sir Thomas Butler, 6th Baronet, politician (d. 1772)
Patrick Duigenan, lawyer and politician (d. 1816)
John McCausland, politician (d. 1804)
Edward Dominic O'Brien, British Army officer (d. 1801)
January 25 - Matthew Clerk, Presbyterian minister (b. 1659)
February 26 - Gustavus Hamilton, politician (b. c.1685)
August 4 - George St George, 1st Baron St George, politician (b. c.1658)
August 27 - Peter Browne, Church of Ireland Bishop of Cork and Ross and writer (b. c.1665)
1735 in Ireland Wikipedia
Events from the year 1735 in Ireland.