Terry won bronze in the individual and team events at the 1992 Olympics
Britain's Nicky Hunt and Simon Terry took silver and bronze respectively in the first World Cup tournament of the season in Porec, Croatia.
Canada's Ashley Wallace won a one-arrow shoot-off to pip Hunt to gold in the women's compound event after the deciding set in the final ended level.
Terry was third in the men's recurve event after thrashing France's Jean Charles Valladont 6-0 in a play-off.
USA's Brady Ellison and Victor Wunderle took gold and silver respectively.
"Finishing in a medal-winning position is a great start to the World Cup series, and I'm delighted to take the bronze," said Lincolnshire archer Terry, a double bronze medallist at the 1992 Olympics in Barcelona and a runner-up in last year's Grand Final in Denmark to Italian Marco Galiazzo.
"It sets me up well for the rest of the campaign, and obviously my goal is to make it through to the Grand Final in September for the second year running."
2009 World Cup finalist Hunt, who lives in Ipswich, had been aiming to reclaim the gold she won last year in Porec.
"It was disappointing not to win another gold medal at this event, but I'm pleased with the way I performed this week, and it's a good start to the World Cup campaign," she said.
This year's Grand Final takes place in Edinburgh in September.