Why Tom sturridge get the role as Edward Cullen in Twilight movie?

Tom Sturridge did not play Edward Cullen in the Twilight movies.

That role was played by Robert Pattinson.

It's likely you're thinking of Tom Sturridge because of his role as the character Lucifer Morningstar in the Netflix series "The Sandman," which has a similar aesthetic to the Twilight movies with its focus on dark fantasy and romance.