The son of a wealthy farmer/businessman, Maggs shot to prominence in Ken Tyrrell's Formula Junior Cooper-Austin team in 1961, sharing the European Championship with Jo Siffert. He was invited into the works Cooper Formula 1 team for 1962 and 63, partnering Bruce McLaren and finishing second in the French Grand Prix of both years. Maggs was dropped at the end of '63 in favor of former World Champion Phil Hill, then drove three races in the Centro-Sud BRM team during the following year and completed his Formula 1 swan song in the 1965 South African Grand Prix at the wheel of a Parnell team Lotus-BRM. Tony then drove in some Formula 2 races later in 1965 before an accident at Pietermaritzburg in a Lotus 22 twin-cam resulted in the death of a spectating child. Thereafter he quit to concentrate on farming in the Zontspanberg region of the Northern Transvaal, surviving a light aircraft accident some years later in which his farm manager was killed.