Charlotte Dujardin won a record-equalling fifth Olympic medal as Great Britain's dressage team took bronze in the team final at Tokyo Equestrian Park.
It was Britain's third successive Olympic team medal in the sport, while 36-year-old Dujardin matched the best Olympic medal haul for a British woman of five achieved by rower Dame Katherine Grainger.
Dujardin, riding major championship debutant Gio, anchored the British team's performance, posting a score of 2617 points for third place, just 24 points overall behind the United States.
Hester, the oldest member of Team GB at 54 and contesting his sixth Games, scored 2577.5 with En Vogue.
And 25-year-old Fry, whose late mother Laura competed for Great Britain at the 1992 Barcelona Olympics, registered 2528.5 aboard Everdale.
Germany made it nine team crowns from the last 10 Olympics as a powerhouse trio of Isabell Werth, Jessica Von Bredow-Werndl and Dorothee Schneider triumphed.
Werth, 52, became the first rider to win seven Olympic golds, and just the third athlete to collect gold at six different Games.
It was an impressive achievement by the British trio, with Fry making her Games bow and all three team horses having never previously competed at an Olympics.
And for Dujardin, it continues a remarkable success story, having won double gold at London 2012 and individual gold and team silver in Rio five years ago on the now-retired Valegro.
She also holds all three world records in the sport, and will now go for a possible sixth Olympic medal in Wednesday's individual freestyle final.
Reflecting on a podium finish in her first Games, Fry said: "I couldn't have asked for much more.
"But I really love competing, and this arena is so amazing to ride in, even without people.
"I didn't really know what to expect, coming here, but being with Carl and Charlotte, they have experienced it all before and they've given me so much support."
Hester added: "That was cool. I had a great balance with En Vogue, and I feel he came here as a boy and he went in there like a man.
"It still feels like he is one of the best horses you could ever sit on. He is amazing.
"We've always known he is so talented, and I have just been waiting for the right ride so I could just prove what we know we think he is."