Félix da Costa began in karting before moving into circuit racing in 2004, when he competed in the Formula BMW UK championship with Carlin Motorsport. He spent two seasons in the series, finishing 13th and then tenth in the championship standings. In 2006 he moved into Formula Renault, competing in both the Formula Renault 2.0 Northern European Cup and the Eurocup Formula Renault 2.0. His younger half-brother António would later win the Northern European Cup in 2009. Despite three years of single-seater competition, Félix da Costa did not record a race win in that category.
Having not translated his pace into victories in single-seaters, Félix da Costa shifted focus to touring cars in 2007, entering the SEAT León Supercopa one-make series and finishing ninth. He returned to SEAT machinery in 2008 in the SEAT León Eurocup, again finishing the season ninth. That same year his performances at Oschersleben in the Eurocup earned him a one-off guest drive in the World Touring Car Championship with Sunred Engineering.
In 2009 Félix da Costa committed to the Portuguese Touring Car Championship, posting his most competitive domestic season with three victories and a final classification of second in the standings. He also made his first foray into sports car racing that year, racing in the International GT Open alongside Miquel Julià in a Ferrari F430 GT3 for Escudería Roger Racing. Additionally, he represented British Touring Car Championship outfit Bamboo Engineering in the European Touring Car Cup at Braga, sharing a Chevrolet Lacetti with Harry Vaulkhard. The pair qualified on the second row and finished eighth and seventh across the two races.
Félix da Costa returned to the SEAT León Eurocup in 2010, completing the season in sixth position.
In 2011 Félix da Costa joined Leipert Motorsport in the Blancpain Endurance Series, co-driving a Lamborghini Gallardo LP600 GT3 with fellow Portuguese drivers Lourençco da Veiga and Ricardo Bravo. The trio finished third in the GT3 Pro-Am class. He made a further sports car appearance in 2012 at the American Le Mans Series round at Monterey's Laguna Seca circuit, finishing 31st in the LMP2 category.
In 2018 Félix da Costa returned to the International GT Open for the Monza round, racing for Drivex School in a Mercedes-AMG GT3 alongside Ricardo Baptista.
From 2013 onwards Félix da Costa transitioned primarily into coaching, working with young drivers navigating junior formulae and sports car categories. The establishment of Synergy Driver Performance in 2015 with co-founder Rodrigo Loyo formalised this role, providing a structured programme for developing drivers progressing through the ranks of European motorsport.
Félix da Costa is married to psychologist Carlota Rocha. His younger half-brother António is a racing driver best known for his success in Formula E; Duarte also serves as António's manager.
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