Dara Morgan, a millionaire businessman from Derry in 2009, frequently wined and dined with "the Trumps, Gateses, de Rothschilds, Gettys and half a dozen more movers and shakers". (PROSE: Beautiful Chaos)
In August 2016, U.S. President Barack Obama condemned Donald Trump as an unsuitable candidate for president. (PROSE: Buccaneer) In 2016, the British youth considered him to be unstoppable. (PROSE: What She Does Next Will Astound You)
In December 2016, after discovering that the Jezrafeq were controlling the minds of most of humanity, Andy Hansen jokingly asked Erimem, "You don't think this could explain Brexit and Donald Trump, do you?". Later, while tracing the source of the mind control signal, Andy suggested that the signal may have been coming from Trump Tower "because [Donald Trump] and Nigel Farage want[ed] to piss [Andy] off even more before the year end[ed]". (PROSE: Cliff Richard Saves the World)
By 2017, Trump had become the president. Bill Potts mentioned that she would have never voted for him as he was "orange". (TV: The Pyramid at the End of the World) Shortly after, Trump was one of the many individuals on the Monks' propaganda machine. (TV: The Lie of the Land)
On 5 May 2018, Alistair Gordon Lethbridge-Stewart, while possessing the body of Hobo Kostinen, read a news article titled "Trump Knew of Payments Months Before He Denied Them". Alistair was shocked to learn Trump had become president in the years since his death, branding Trump an "oaf". (PROSE: Lucy Wilson and the Bledoe Cadets)
Behind the scenes
In DWM 503, Steven Moffat, the showrunner of Doctor Who from series 5 to 10, answered the question, "What does the Doctor make of Donald Trump's decision to run for President of the United States?" Moffat replied that "although the Doctor normally takes no part in politics, he is disgusted and turbulent with rage" and went on to say that the Doctor has seen a parallel universe in which Trump won the election and the world was plunged into "certain doom".
In the real world, Trump did in fact win the election, and was president from 20 January 2017 to 20 January 2021. However, an unnamed president in a simulation created by the Monks in the 2017 episode Extremis was a dark haired individual who did not have much physical resemblance to Trump. According to Moffat, the writer of Extremis, Extremis was written before but filmed after the 2016 election.
In The Pyramid at the End of the World, Bill Potts says she would have never have voted for the current president, as he's "orange". While Trump was left unnamed, it was clearly referencing Trump and his spray-tans.
The 2017 episode The Lie of the Land features an image of Trump clearly visible on one of the screens inside the room that houses their propaganda machine along with several other prominent contemporary and historical figures. Trump is later stated to have become president in the DWU by 2018, when the episode Arachnids in the UK is set.
In the 2019 audio story Sargasso, the American character Kaitlin Russell refers to the very real possibility of "some asshole with bad hair" blowing the world to hell, along with other approaching catastrophes.