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The film, produced by Disneynature, is one of a series of films intended to be released for Earth Month. "Elephant" follows an elephant family through the Kalahari Desert on a 1,000-mile trip.
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The British newspaper reported that the deal was for Meghan to do voice-over work in return for a donation to Elephants Without Borders -- which tracks and protects elephants.
In January, a video resurfaced from the premiere of "The Lion King" last summer that showed Prince Harry promoting Meghan's voice-over ability to then-Disney CEO Bob Iger.
Meanwhile, Meghan was chatting with pop icon Beyonce, who voiced Nala in "The Lion King," according to British newspaper The Telegraph.
Disney+ also announced Wednesday that a film about dolphins would also be released on April 3. "Dolphin Reef," is narrated by actress Natalie Portman.
When Harry and Meghan announced they were giving up their royal duties, they also said they would seek financial independence.
The couple -- with their 10-month old son Archie -- have been living on Vancouver Island since late last year. Speculation remains as to where they will end up settling down.
They were married in May 2018 at Windsor Castle. Prince Harry is the grandson of Queen Elizabeth II.
The Associated Press contributed to this report.