Renown, like the other Resolution-class submarines, was ordered on 8 May 1963 and was laid down at Cammell Laird's Birkenhead shipyard on 25 June 1964.

[1] Construction was slower than planned, with poor performance by Cammell Laird and its workforce resulting in both Renown and sister ship Revenge being delayed.

In 1966, it was discovered that due to lax interpretation of drawings, Renown's torpedo storage compartment differed in length by 1 inch (2.5 cm) from the lead ship Resolution, and in November that year, broken bits of metal were found in the submarine's primary cooling circuits, the removal of which delayed construction by two months.

[5] Renown struck the entrance to a dock when leaving Lairds for sea trials in February 1969, and collided with a merchant ship, MV Moyle in the Irish Sea on 13 October 1969, which resulted in Renown's commanding officer being found guilty of hazarding his submarine at the resulting court-martial and relieved of command.

[7] Following a refit Renown carried out test firings of Chevaline, which was a modification of the Polaris missiles to enable them to penetrate Soviet anti-ballistic missile defences, in early 1982, and was fully operational with Chevaline late that year.