In 2016, Depp played businessman and U.S. presidential candidate Donald Trump in a Funny or Die satire film entitled Donald Trump's The Art of the Deal: The Movie. He earned praise for the role, with a headline from The A.V. Club declaring "Who knew Donald Trump was the comeback role Johnny Depp needed?" The same year, Depp reprised the role of the Mad Hatter in Alice Through the Looking Glass, the sequel to Alice in Wonderland. Depp was secretly cast to play Gellert Grindelwald in a cameo appearance in the 2016 film Fantastic Beasts and Where to Find Them, a role he was expected to reprise in all future sequels. Grindelwald is a dark wizard who once shared a close relationship with Albus Dumbledore, a major character in the Harry Potter film series. Depp was also cast as Dr. Jack Griffin / The Invisible Man in Universal Studios' planned shared film universe entitled the Dark Universe, a rebooted version of their classic Universal Monsters franchise. After the first film of the series, The Mummy (2017), received generally negative reviews from critics and performed below the studio's expectations at the box office, producers Alex Kurtzman and Chris Morgan left and Universal put the franchise on hold. In 2019, it was reported that Depp was no longer attached to the project.
In November 2016, Depp teamed with David Lynch, J. K. Simmons, Laura Dern, Penelope Ann Miller, Chad Coleman, Richard Chamberlain, Catherine Hardwicke, Theodore Melfi, Sam Raimi, Peter Farrelly, and the non-profit Make a Film Foundation for a volunteer project entitled The Black Ghiandola, a short film written by Anthony Conti. The movie is "a story about a young man risking his life to save a young girl he has grown to love, after his family has been killed in the Apocalyptic world of Zombies." The film was released in April 2017. The same year, Depp reprised his role as Captain Jack Sparrow in the fifth installment of the Pirates series, Pirates of the Caribbean: Dead Men Tell No Tales. He also co-starred as part of an ensemble cast in the Agatha Christie adaptation Murder on the Orient Express (2017), as Edward Ratchett.
In 2016, then-wife Amber Heard claimed that Depp "plunged into the depths of paranoia and violence after bingeing on drugs and alcohol," although a joint statement issued by Heard and Depp in connection with their divorce denied that either party intended "physical or emotional harm" to the other. In 2018, reporter Stephen Rodrick of Rolling Stone wrote that Depp had used hashish in his presence and described Depp as "alternately hilarious, sly and incoherent"; Rodrick also quoted Depp as stating that a claim that he had spent US$30,000 per month on wine was "insulting" because he had spent "far more" than that amount. During his 2020 libel trial, Depp admitted to having been addicted to Roxicodone and alcohol in the 2010s.
In April 2016, Heard appeared in a magistrates' court in Southport, Queensland pleading guilty to falsifying quarantine documents, stating that she was sleep deprived and made a mistake. The two biosecurity charges were dropped, and she was placed on a one-month good behaviour bond, paying an A$1,000 fine for producing a false document. Heard and Depp also released a video in which they apologized for their behavior and urged people to adhere to the biosecurity laws. The Guardian called the case the "highest profile criminal quarantine case" in Australian history.
In March 2016, Depp cut ties with his management company, The Management Group (TMG), and sued them in January 2017 for allegedly improperly managing his money and leaving him over $40 million in debt. TMG stated that Depp was responsible for his own fiscal mismanagement, alleging that he had spent over $2 million monthly, and countersued him for unpaid fees. In a related suit, Depp also sued his lawyers, Bloom Hergott, in January 2017. Both lawsuits were settled, the former in 2018 and the latter in 2019.
In November 2016, Depp joined the campaign Imprisoned for Art to call for the release of Ukrainian filmmaker Oleg Sentsov, who was being held in custody in Russia.