The Red Bull junior, who won a Formula Renault 3.5 race at Monza last weekend, will fill in for Buemi, who is racing with Toyota in the World Endurance Championship season opener at Silverstone.
Buemi has attended grands prix in the role since he lost his Toro Rosso drive at the end of the 2011 season.
He has an expanded sportscar racing programme with Toyota this year, but the Silverstone round round is the only WEC event that clashes with a grand prix.
Da Costa was recruited by Red Bull last summer as a replacement for Lewis Williamson on its junior scheme.
The 21-year-old narrowly missed out on the GP3 title at the end of 2012, but he did win four of the last five FR3.5 races and take victory in the prestigious Macau Grand Prix Formula 3 race.
He sits third in the FR3.5 standings after last weekend's opening round, trailing McLaren juniors Stoffel Vandoorne and Kevin Magnussen in the points.