Person of colour

The term "person of colour", or POC, at least in the United States, referred to any person who was not white.

Rachel Edwards was not pleased to find only a couple of POCs in Matt Nelson's entourage of otherwise invariably white, cisgender, monosexual rich people. (PROSE: Head of State)

Companions
Sharon Davies holds the title of first recurring companion of colour, introduced in the 1980 comic Doctor Who and the Star Beast. She is predated only by Nick Willard, who served as a companion in the 1973 comic Zeron Invasion alone.

Mickey Smith and Martha Jones, played by Noel Clarke and Freema Agyeman, later became the first companions of colour on television, in series 2 (2006) and series 3 (2007), respectively.

Since then, Bill Potts was introduced in series 10 (2017), and both Yasmin Khan and Ryan Sinclair were introduced in series 11 (2018).

The Master
Series 12 (2020) introduced Sacha Dhawan as the first non-white actor to play on television.

The audio story Mastermind (2013) previously saw the Master voiced by Yee Jee Tso, in one of the Master's stolen bodies, and the Doctor Who: The Eleventh Doctor Year Two comics (2016) introduced the Master's first Time War incarnation, who had the appearance of an East Asian child.

The Doctor
Series 12 also introduced the Fugitive Doctor, an incarnation wrapped in mystery, who was played by Jo Martin. Martin became the first actor of colour to be cast in the role of the Doctor, making this Doctor the first non-white incarnation to make an appearance in any performed medium. Before Fugitive of the Judoon (2020), every incarnation of the Doctor had been primarily played by a white actor, most often by a white man.

The same series also revealed that the Doctor had lived countless regenerations before the First Doctor, in the form of the Timeless Child. Multiple actors of colour portrayed the character in The Timeless Children. In fact, before Jo Martin hit the screens, the First Timeless Child appeared in a memory, as a young black girl, though her identity would not be confirmed until the series finale.

Steven Moffat revealed in Doctor Who Magazine that he intended the character of Doctor Moon, played by Colin Salmon, to be a future incarnation of the Doctor. Though Russell T Davies noted he also viewed the character this way, this relationship has ever been confirmed in a narrative source.

Other roles
The Burmese-born actress Zienia Merton portrayed Ping-Cho in Marco Polo (1964) making her the first person of colour with a speaking role in the shows history. However, due to all of the serial being missing from the records, with only pictures surviving, it is difficult to say which actor of colour was the first to appear on screen, though it might be one of Tegana's entourage when they confront the TARDIS team in the same story.

DWU crew
Behind the camera, the director of Doctor Who's very first serial, An Unearthly Child (1963), Waris Hussein, was a man of colour.

The first writer of colour for the franchise was Noel Clarke, with Combat. However, Malorie Blackman and Vinay Patel became the first writers of colour to contribute scripts to Doctor Who itself, in series 11 (2018). They wrote Rosa and Demons of the Punjab, respectively.

That same series, Mark Tonderai became the first black director, and Segun Akinola became the first person of colour to serve as composer for the series.