Courage was the eldest son of Richard Courage, Lord of the Manor of Edgcote, and heir to the Courage brewing dynasty. Educated at Eton College, he began racing in his own Lotus 7 and briefly toured European Formula Three events in 1964 with a Lotus 22. In 1965 he drove a 1.0-litre Formula Three Brabham for Charles Lucas, where he first formed a working alliance with Frank Williams, then Lucas's other driver and sometime mechanic. That season produced four high-profile wins and caught the attention of Colin Chapman, who offered Courage a Lotus 41 for the 1966 F3 season.
His F3 results, combined with a step up to Formula Two at the 1966 German Grand Prix, led to a works BRM contract for 1967 alongside Chris Irwin. A tendency to crash and spin in the early races led BRM to drop him after the Monaco Grand Prix, and he completed the season in John Coombs's Formula Two McLaren M4A, finishing fourth in the unclassified championship. A strong winter Tasman Series campaign, including a race win, secured him a drive with Tim Parnell's works-supported Reg Parnell Racing BRM team for 1968. He also drove for Frank Williams's Formula Two operation that year.
When Frank Williams Racing Cars stepped up to Formula One in 1969, Courage was the natural first choice as driver. The team purchased a Brabham BT26, painted it in dark blue livery, and entered it under the Frank Williams banner. The combination proved more competitive than its privateer status suggested.
Courage finished second at the Monaco Grand Prix and second again at the United States Grand Prix at Watkins Glen. At the 1969 Italian Grand Prix at the high-speed Monza circuit, he kept pace with the leading group in an older, less powerful car until fuel starvation slowed him near the finish; he classified fifth. A fifth place at the British Grand Prix completed a season total of 16 championship points, leaving him eighth in the Drivers' Championship standings.
For 1970, Williams entered into a business arrangement with Alejandro de Tomaso and switched to a newly designed De Tomaso chassis. The car proved overweight and unreliable. Only a third place in the non-championship International Trophy offered any encouragement from the opening part of the season.
At the Dutch Grand Prix at Zandvoort on 21 June 1970, Courage qualified ninth. Running in the midfield, the De Tomaso's front suspension or steering failed at the high-speed Tunnel Oost bump, sending the car straight rather than through the corner. It rode up an embankment and disintegrated on impact. The chassis, which used magnesium components to save weight, ignited on contact with the wreckage and burned intensely, setting nearby trees and bushes alight. During the impact, a front wheel broke free and struck Courage in the head, tearing away his helmet. He died at the scene. He was survived by his wife, Lady Sarah Marguerite Curzon, and their two sons.
The death of Piers Courage ended Frank Williams's partnership with de Tomaso and marked a pivotal moment in the team's history. Williams persisted through lean years before co-founding Williams Grand Prix Engineering with Patrick Head in 1977, the organisation that went on to win nine Constructors' Championships.
Courage's 1969 performances remain notable for the competitive return achieved on a tight budget: two podium finishes from a customer car in a field dominated by works teams represented genuine merit rather than fortune. His career trajectory, and the manner of his death in a lightweight chassis on fire, contributed to the technical and safety debates that slowly began reshaping Formula One construction standards in the 1970s.