On his father's death in 1771 Nevill took over the latter's Wexford seat, representing the borough until Ireland became part of the United Kingdom in 1801. He was appointed High Sheriff of Kildare for 1773–74.
He was appointed to the sinecure position of Teller of the Irish Exchequer from 1801 to 1806 and was then restored to the position from 1807 until his death.
He continued to represent Wexford Borough in the UK Parliament from 1802 to 1806, from 1807 to 1810, from 1811 to 1813 and from 1814 to 1819, alternating with other representatives on account of his age and health.
He died in 1822. He had married Bridget, the daughter and heiress of Henry Bowerman of Cooliney, co. Cork, and had 4 daughters. Furness was left to daughter Marianne, who sold it to the Beauman family.
- "NEVILL, Richard (1743-1822), of Furness, co. Kildare". History of Parliament Online. Retrieved 21 May 2016.
- "A Gentle Evolution". The Irish Aesthete. Retrieved 21 May 2016.