Cartier initially trained as an architect, but an enthusiasm for drama and the theatre led him to changing career paths. He enrolled in the Vienna Academy of Music and Dramatic Arts, where he was taught by Max Reinhardt, and later moved to Berlin. Here he began his career in the film industry, in 1929 joining the famous UFA studios home to such luminaries as Emeric Pressburger, where he worked initially as a scriptwriter.

By 1936, the rise of the Nazi party to power in Germany had made it difficult for Cartier, who opposed their views, to remain in the country. He moved to the UK, where several unsuccessful attempts to make his way in the film industry as a producer and director led to a barren spell in his career leading up to and during the Second World War. Following the war he went for a time to the United States, studying the methods they used there in making both film and the newer medium of television.

In the early 1950s, Cartier was hired by BBC Television's Head of Drama Michael Barry as a television director, in spite - or perhaps because of - the fact that at his interview, Cartier had told Barry that he thought the output of his department was awful, too reliant on theatrical techniques and not taking advantage of the possibilities television offered.

Cartier went on to become the BBC's premier director of television drama over the course of the decade, developing many techniques that are now standard in the medium today and pushing the then primitive technicalities of the television studios to their limits. He used an increasing amount of pre-filming work on location to give his productions a scope and scale the live electronic studio environment did not allow, although he was also an accomplished exponent of the multi-camera studio system then predominant. His high standards, however, did earn him a reputation in some quarters as a perfectionist who was difficult to work with.

Cartier formed a particularly productive partnership with the scriptwriter Nigel Kneale. Kneale was a BBC television staff writer who was brought in to polish up Cartier's own adaptation of a German short story, Arrow to the Heart, in 1952. This was the first of many productions together, and the following year they teamed up to produce the legendary science-fiction serial The Quatermass Experiment, introducing complex, original, adult-oriented science-fiction to the television audience for the first time.

In 1954, Kneale and Cartier's new-found reputation for science-fiction led Michael Barry to assign them the task of handling an adaptation of George Orwell's famous dystopian novel Nineteen Eighty-Four. A highly praised but also controversial production, it sealed Cartier's place in the annals of television history, and in 2000 was included in a poll of industry professionals conducted by the British Film Institute to find the 100 Greatest British Television Programmes.

Further collaborations with Kneale followed. There were two more Quatermass serials, Quatermass II (1955) and Quatermass and the Pit (1958-59, also featured in the BFI 100 Greatest list), an adaptation of Wuthering Heights and another Kneale original, The Creature. Cartier also pursued his passion for opera, directing epic televised versions of such operas as Otello (1959) and Carmen (1960).

Cartier continued directing highly esteemed television dramas for the BBC throughout the 1960s. Some of his most famous productions during this decade included: a version of Anna Karenina, starring Sean Connery, in 1961; Cross of Iron (also 1961), a play about the real-life court-martial of a U-Boat captain in a British prisoner-of-war camp during the Second World War; The July Plot (1964), about the 1944 plan of several Nazi Generals to assassinate Adolf Hitler, and Lee Oswald - Assassin, a 1966 drama documentary telling the story of JFK's killer.

Cartier's last television work was Gaslight in 1977, bringing to an end twenty-five years as a director for the BBC. He never worked in commercial television, as he despised the idea of advertisements interrupting his productions. He died in 1994, at the age of ninety, and in tribute the BBC re-screened his version of Nineteen Eighty-Four, accompanied by a documentary on his work. It is difficult to imagine such an honour being accorded to any other director who worked exclusively in the medium of television, usually seen as more of a writer's medium than a director's, and the directors who work in it as the poorer cousins of their cinema counterparts. Cartier had successfully bucked this trend, to become one of the most successful directors of his era.