The phrase "as a direct sequel" is correct and usable in written English.
It can be used when referring to a work that continues the story or themes of a previous work without significant time gaps or changes in narrative style.
Example: "The new film is being marketed as a direct sequel to the original, picking up right where the last one left off."
Alternatives: "as an immediate follow-up" or "as a straightforward continuation".
The film, directed by Yutaka Uemura, saw many of the anime's voice actors reprise their roles and serves as a direct sequel to the TV show.
New Vegas in 2010 was quite similar to Fallout 3 in gameplay, graphics and mechanics, and in fact doesn't count as a direct sequel (hence Fallout 4).
We also get a ten-minute preview of the next DCAU feature, which will serve as a direct sequel to Justice League: War and introduce Aquaman to the fold.
Forty years after the original, the 11th "Halloween" movie serves as a direct sequel to John Carpenter's 1978 horror classic.
The story continues from the events in Tomb Raider: Legend as a direct sequel, but also addresses unexplained plot elements by association with Tomb Raider: Anniversary.
Ten years later, O'Brien wrote another script intended as a direct sequel to the cult classic entitled Revenge of the Old Queen.
Already playing in some markets overseas, the sequel to James Cameron's brilliant franchise that established Arnold Schwarzenegger as a true movie star is intended as both a direct sequel to Cameron's first two movies (the third and fourth were made without his involvement, and didn't get a very enthusiastic endorsement from the filmmaker) and a reboot of the whole storyline.
Make-up artist Louis Lazzara, who cites A New Beginning as almost a direct sequel to The Final Chapter, did base his head-mask on Tom Savini's design for The Final Chapter.
Langan described the film as not being a direct sequel, only that it reunited the same creative team.
Although Police Surgeon was not a success and was cancelled after only a short run, Newman took Hendry as the star, and some of the ethos of the programme, to create a new series (not a direct sequel as is sometimes claimed) called The Avengers.
After the release of Conker's Bad Fur Day, Rare began development of a direct sequel referred to as Conker's Other Bad Day, but it was ultimately cancelled.
