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The film, from Chilean director Pablo Larrain, is set over a weekend in the early 1990s when Diana joined the royal family for Christmas at the Queen’s Sandringham Estate.
Set to the soundtrack of a cover version of the Lou Reed song Perfect Day, the trailer shows cars arriving and outfits laid out as food is unpacked and prepared before the royal family sit down for a meal.
Meanwhile, Diana is locked in a bathroom in distress, as she is told: “Ma’am, they are waiting for you.”
She can be seen walking down the corridor in a glamorous white gown, which she is wearing on the movie’s poster, and posing with the rest of the family for a group photo.
It also shows her being mobbed by photographers, walking alone in the gardens and dancing in a palace.
She can also be seen being comforted by another woman, played by Sally Hawkins, with whom she frolics on a beach and embraces.
The trailer ends with Hawkins telling her, “They know everything,” to which Stewart replies: “They don’t.”
The footage also gives a first look at Poldark star Jack Farthing as Charles.
The cast also includes Timothy Spall and Sean Harris.
Diana died aged 36 in 1997 following a car crash in Paris.
The 24th anniversary of her death is on Tuesday.
Spencer will be released in UK and Irish cinemas later this year following its world premiere at the Venice Film Festival on September 3.