He was eldest son of Alexander Napier, sixth of Merchiston, who was killed at the battle of Pinkie in 1547. His mother was Annabella, youngest daughter of Sir Duncan Campbell of Glenurchy. His paternal grandfather was Sir Alexander, fifth of Merchiston, who was killed at the battle of Flodden in 1513. Archibald was infeft in the barony of Edenbellie as heir to his father on 8 November 1548, a royal dispensation enabling him, though a minor, to feudalise his right to his paternal barony in contemplation of his marriage with Janet Bothwell, which took place about 1549. Napier began to clear his property of encumbrances. On 1 June 1555 he redeemed his lands of Gartnes, Stirlingshire, and others from Duncan Forester, and on 14 June 1558 he obtained a precept of sasine for infefting him in the lands of Blairwaddis, Isle of Inchcolm. In 1565 he received the order of knighthood. He seems to have sided with Mary Queen of Scots after her escape from Lochleven Castle. During the siege of Edinburgh Castle, held by Kirkcaldy of Grange for the queen, he was required on 1 May 1572 to deliver up his house of Merchiston to the king's party, who placed in it a company of soldiers to prevent victuals being carried past it to the castle. On this account the defenders of the castle made an attempt to burn it, which was unsuccessful.
At the cunzie-house
Napier's name appears with others in a contract with Regent Morton for working for the space of twelve years certain gold, silver, copper, and lead mines. He was appointed general of the cunzie-house in 1576, and on 25 April 1581 he was directed, with others, to take proceedings against John Achesoun, the king's master-coiner. In May 1580 he received payment for the expenses of a mission to England. On 24 April 1582 he was named one of the assessors to prepare the matters to be submitted to the general assembly of the kirk of Scotland, and his name occurs in following years as an ordinary member of assembly, and also as acting on special commissions and deputations. On 6 March 1590 Napier was appointed one of a commission for putting Acts in force against the Jesuits. In January 1593 he was appointed by a convention of ministers in Edinburgh one of a deputation to wait on the king to urge him to more strenuous action against the Catholic nobles, and he was appointed one of a similar commission at a meeting of the general assembly of the kirk in April, and also by a convention held in October.
Last years
On account of non-appearance before the council of his son Alexander, charged with a serious assault, Napier was on 2 July 1601 ordained to keep ward in Edinburgh until King James declared his will. In September 1604 he went to London to treat with English commissioners about the Mint, when, according to Sir James Balfour, he negotiated skillfully. Napier continued till the end of his life to take an active part in matters connected with mining and the currency. He discussed samples of gold ore with the English prospector George Bowes in 1604. On 14 January 1608 he was appointed along with two others to repair to the mines in succession to try the quality of the ore. He died on 15 May 1608, aged 74.
Family
By his first wife Janet, only daughter of Francis Bothwell, lord of session, by his first wife Janet Richardson, Napier had two sons and one daughter:
Archibald Napier of Woolmet, ambushed and slain on 8 November 1600 in revenge for the murder of Scott of Bowhill in an argument over a horse, widowing his young wife Alison Edmonstone of Edmonstone House
Elizabeth, married, first, to James, lord Ogilvie of Airlie, and, secondly, to Alexander Auchmoutie, gentleman of his majesty's privy chamber.
On 8 February 1588 the king granted to Napier, Elizabeth Mowbray, his second wife, and Alexander, their son and heir, the lands called the King's Meadow. On 16 November 1593 he obtained a grant of half the lands of Lauriston, where he built Lauriston Castle.