Alien (1979) was directed by Ridley Scott, but after that in 1986 Aliens was written and directed by James Cameron.
Why didn't the studio offer Ridley Scott the chance to direct the 2nd Alien movie?
From alienseries, the producer blamed it on availability:
In 1986 Bobbie Wygant asked Aliens producer Gale Anne Hurd if Scott had turned down the opportunity to direct the sequel. “I’m not really sure,” Hurd answered. “I know that he was in post-production on Legend at the time we were in pre-production [on Aliens], so perhaps it was a result of his availability.”
But that wasn't true:
“They didn’t ask me!” he told The Hollywood Interview in 2008. “To this day I have no idea why. It hurt my feelings, really, because I thought we did quite a good job on the first one.”
There are some rumors circulating around but nothing definitive.
We don't know. Gale Anne Hurd said in 1986
I’m not really sure. I know that he was in post-production on Legend at the time we were in pre-production [on Aliens], so perhaps it was a result of his availability
Ridley told The Hollywood Interview in 2008
They didn’t ask me! To this day I have no idea why. It hurt my feelings, really, because I thought we did quite a good job on the first one
There are rumours that Scott have different view on whole Aliens script and with H.R. Giger they envisioned that the second movie would be a prequel telling the story of Space Jockeys and Pyramid.
So maybe there lies an answer. Producers wanted more alienS while Scott wanted more lore at the cost of not even showing one alien.
Also, Scott's 1982 film Blade Runner was not nearly as big a financial success (at the time) as Alien, so it's possible that the idea of him directing was not as easy a sell. Scott's 1985 film Legend did not make back its investment. Fox execs couldn't have known that when they had to select a director for Aliens, but there was likely a feeling that Scott was not on his game in the early 80s.
Scott was working on Legend at the time the script for Aliens was nearing completion, so Fox execs might have assumed he would decline the offer and there was no point in asking.
From the Wikipedia page on Aliens:
While the producers and development executive Larry Wilson sought a writer for Alien II, Wilson came across James Cameron's screenplay for The Terminator, and passed the script to Giler, feeling Cameron was right for the job. Giler then approached Cameron, who was completing pre-production of The Terminator. A fan of the original Alien, Cameron was interested in crafting a sequel and entered a self-imposed seclusion to brainstorm a concept for Alien II. After four days Cameron produced an initial 45-page treatment, although the Fox management put the film on hiatus, as some disliked the pitch, and they felt that Alien had not generated enough profit to warrant a sequel. A scheduling conflict with actor Arnold Schwarzenegger caused filming of The Terminator to be delayed by nine months (as Schwarzenegger was filming Conan the Destroyer), allowing Cameron additional time to write a script for Aliens. While filming The Terminator, Cameron wrote 90 pages for Aliens, and although the script was not finished, Fox's new president Larry Gordon was impressed and told him that if The Terminator was a success, he would be able to direct Aliens.