You might have realized that the main verb in the sentence 'wrote' is a tautology - the play would not exist unless Sheriff had written it! So this is probably better:
In 1929, the English playwright R. C. Sheriff (1896-1975), who had been wounded during the First World War, depicted the psychological impact of the trenches on a group of young recruits in his famous anti-war play, Journey's End.
As you get more confident, you can be more ambitious. Consider this:
Although the English playwright R. C. Sheriff (1896-1975), who had been wounded during the First World War, is best known for depicting the psychological impact of the trenches on a group of young recruits in his anti-war play of 1929, Journey's End, his later film scripts, notably for The Dambusters (1955), take a more conventionally heroic view of combat.
Or even this,
To understand why the English playwright R. C. Sheriff (1896-1975), who had been wounded during the First World War and is best known for his anti-war play of 1929, Journey's End, which depicts the psychological impact of the trenches on a group of young recruits, took a more conventially heroic view of combat in his later film scripts, notably for The Dambusters (1955), we must explore the diverging conventions of cinema and theatre after the Second World War, and Sheriff's own emotional development.
This is probably too long a sentence. It is included to illustrate how much a sentence can do. You should have high expectations of a sentence, and not be satisfied until it has earned its full stop.
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