The forthcoming Bond film will see actress Lashana Lynch play a female 00 agent after Craig's Bond has left active service.
Lynch was seen in character for the first time in the trailer, reigniting the conversation about whether James Bond himself could be re-cast as a woman for the next film.
Broccoli oversees the franchise with her half-brother Michael G Wilson. "For better or worse, we are the custodians of this character," she said. "We take that responsibility seriously."
The pair reflected on how the Craig era has altered the direction of the franchise.
Pierce Brosnan's final Bond film, 2002's Die Another Day, was a financial success but was criticised for pushing the boundaries of realism.
The film's plot involved a giant space laser and an invisible car.
"We got too fantastical," says Wilson, referring to the film. "We had to come back to Earth."
Craig's era has, in contrast, more closely resembled the original character Ian Fleming wrote.
Martin Campbell, the director of GoldenEye and Casino Royale, admitted he was not convinced Craig was the correct choice to begin with, but came around with Broccoli's persuasion.
"To be honest, it took me a little while to see it," he said. "Daniel's acting was terrific, but he wasn't a pretty-boy. Barbara was adamantly in favour of him."
Craig had originally indicated he would not return to the series, but agreed to film one more after speaking with Broccoli.
"Barbara doesn't take no for an answer," said Craig. "It's not in her wheelhouse."
"I had a nice long break, which I really needed. And then she was just persistent and came to me with some ideas, which we started formulating, and I got excited again."
"No Time to Die" will be Craig's fifth 007 film, with Oscar winner Rami Malek taking on the role of the villain.
Ralph Fiennes, Rory Kinnear, Ben Whishaw, Naomie Harris, Lea Seydoux and Jeffrey Wright will all return for the 25th movie in the popular film series.