She hasn't said what the topic is, just that it's another historical theme. Doesn't being a producer mean that you invest financially in a film?
Fearless Sarah, Duchess of York returns behind the camera - Telegraph
According to one source:
What does a producer do, exactly?
He shepherds the production from start to finish. In a typical arrangement, the producer develops an idea or script with a writer and secures the necessary rights. He often hires the director, supervises casting, and assembles a crew. Additionally, the producer oversees the budget and then coordinates the postproduction work—everything from editing, to commissioning music, to encouraging the film's stars to plug the movie on talk shows.
The top post of "producer" is just the tip of the iceberg, as anyone who's watched the opening credits of a movie knows well. Although
Slumdog Millionaire, for example, credits only one producer, it lists two executive producers and two co-executive producers, along with a co-producer, an associate producer, and a line producer.
An executive producer often owns the rights to a book or story idea or secures at least 25 percent of the film's budget. Executive producers rarely have creative or technical involvement and are often caught up with several projects at once. The "co-executive producer" title applies to studio executives or distributors who have a limited financial stake in the project. A co-producer works under the producer and often helps with casting, financing, or postproduction.
What does a Hollywood producer do, exactly? - Slate Magazine
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So it can actually vary on what Sarah's responsiblities . It looks like its a semi paying job but I don't think producers get paid until the movie makes money.