Paramount Pictures announced it was planning a fourth film starring Chris Hemsworth at the CinemaCon film convention in Las Vegas but did not give away much else.
But according to Variety, Clarkson, who has worked on everything from EastEnders and Casualty to Dexter, Life on Mars and Ugly Betty, will “boldly go where no woman has gone before” for Star Trek 4.
Clarkson’s more recent credits include episodes for shows such as Orange Is The New Black, Marvel series Jessica Jones and British drama Collateral.
While plot details for the upcoming Star Trek film are limited, there will reportedly be some time travel involved with Chris Pine – who plays James T Kirk – running into his father, played by Hemsworth.
Heroes actor Zachary Quinto is also expected to return to the franchise after playing Spock in the first instalment of the film series in 2009.
JD Payne and Patrick McKay, who both worked on 2016’s Star Trek Beyond, have written the screenplay for the upcoming film.
JJ Abrams – who kickstarted the reboot and is also producing Star Wars: Episode IX – will produce Star Trek 4 with Lindsey Weber, who also produced the 2016 film.
The 2009 film brought in $385m (£279m) at the box office worldwide and its 2013 sequel Star Trek Into Darkness generated $467m (£339m).
The third instalment in 2016 earned $343m (£249m) internationally.
Paramount is also developing another Star Trek film from Abrams and Quentin Tarantino but it is still being written, according to reports.
It is expected to be released after the fourth film.
Since it started in 1966, the Star Trek franchise has built a reputation for challenging some stereotypes, including one of the first onscreen US TV kisses between a black woman (Lt Uhura) and a white man (Capt Kirk).