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 2018, Trump had become president. (TV: Arachnids in the UK) On 5 May 2018, Alistair Gordon Lethbridge-Stewart read a news article titled "Trump Knew of Payments Months Before He Denied Them". (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. 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.
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.