Inheriting his father's title on 2 January 1775, Napier was earlier commissioned into the 31st Foot in 1774 and was promoted to a lieutenant in 1776.
In 1796, 1802 and 1807, he was chosen as a Scottish representative peer and was Lord Lieutenant of Selkirkshire from 1797 until his death in 1823.
From 1802 until his death, Napier was, with Henry Dundas, 1st Viscount Melville's help, annually nominated as Lord High Commissioner.
Napier died at his home, Dacre Lodge in Enfield, in 1823 and his title passed to his eldest son, William.
They had five daughters and four sons, including William John (1786–1834), later 9th Lord Napier.