The son of a Police Commissioner of the Shanghai Municipal Police, Young was born in Shanghai, China and was public-school educated. He read oriental history at St Catharine's College in the University of Cambridge.
Young began in the film industry as a screenwriter, earning a credit for On the Night of the Fire (1939), Dangerous Moonlight (1941), Secret Mission (1942), A Letter from Ulster (1942) and On Approval (1944).
Commissioned in the Irish Guards, Young was a tank commander during World War II where he participated in Operation Market Garden in Arnhem, Netherlands.
In 1946, he returned to assist Brian Hurst with the script of Theirs is the Glory, which recaptured the fighting around Arnhem bridge. Arnhem, coincidentally, was home to the adolescent Audrey Hepburn. During the filming of Young's film, Wait Until Dark, Hepburn and Young would joke that he was shelling his favorite star without even knowing it.
Young worked on the screenplays for Hungry Hill (1947) and Bad Lord Byron (1949).
Young's first sole credit as director (and also Christopher Lee's film debut) was Corridor of Mirrors (1948), an acclaimed film made in France. He followed it with a musical One Night with You (1948); Woman Hater (1948) a comedy with Stewart Granger; They Were Not Divided (1950), based on his own story, about the Guards Division.
Young directed Valley of Eagles (1951) and The Tall Headlines (1952).
He then made the first film for Irving Allen and Albert R. Broccoli's Warwick Films, The Red Beret with Alan Ladd. It was a big hit.
Young made That Lady (1955) in Spain with Olivia de Havilland and was hired by Alexander Korda to do an essentially shot-for-shot remake of The Four Feathers (1939), Storm Over the Nile (1955); nonetheless it was popular.
Warwick asked Young back to do a movie about the Mau Mau, Safari (1956) with Victor Mature. For the same company he did Zarak (1957), also with Mature.
MGM hired him to make Action of the Tiger (1957) with Van Johnson; a young Sean Connery had a support role. No Time to Die (1958) was Young's fourth film for Warwick, and third with Mature. He made Serious Charge (1959), which had Cliff Richard's film debut; Too Hot to Handle (1960)with Jayne Mansfield; Black Tights (1961) in France; and Duel of Champions (1961) in Italy with Alan Ladd.
Albert Broccoli and Irwin Allen had split up as a producing team and Broccoli went into partnership with Harry Saltzmann to make a series of films based on the James Bond novels. Broccoli used many crew he had worked with during his time as Warwick for the first Bond movies, including Young as director. Young made a crucial contribution to Dr. No (1962), including the performance of Sean Connery as Bond. Lois Maxwell claimed that "Terence took Sean under his wing. He took him to dinner, showed him how to walk, how to talk, even how to eat."
The movie was a huge success and was quickly followed by From Russia with Love (1962), an even bigger hit. During the filming of From Russia with Love, Young and a photographer nearly drowned when their helicopter crashed into the sea while filming a key sequence. They were rescued by other members of the film crew. Young was back behind the camera thirty minutes after being rescued.
Young was deluged with offers and elected not to direct Goldfinger. Instead he made The Amorous Adventures of Moll Flanders (1965) and did a segment of The Dirty Game (1965).
Young was called back for the fourth Bond, Thunderball (1965).
Young provided the story for Atout cœur à Tokyo pour OSS 117 (1966) and directed the all star The Poppy Is Also a Flower (1966). He followed this with Triple Cross (1966), and The Rover (1967). Young had a hit with Wait Until Dark with Audrey Hepburn.
Young's work was focused in Europe: Mayerling (1968), with Omar Sharif; The Christmas Tree (1969) with William Holden.
He made three with Charles Bronson: Cold Sweat (1970), Red Sun (1972) and The Valachi Papers (1972).
Young's later films include War Goddess (a.k.a. The Amazons) (1973), and The Klansman (1974). He worked on Jackpot but the film was never finished.
Later credits include Foxbat (1977), Bloodline (1979), Inchon (1982) about the Battle of Inchon with Laurence Olivier, The Jigsaw Man (1983) with Michael Caine and Olivier (replacing the original director), and Run for Your Life (1988). Olivier and Young had been friends since 1943 when Olivier had initially offered the direction of his film Henry V (1944) to Young, who declined.
According to Young, he was offered and turned down the direction of For Your Eyes Only and Never Say Never Again.
Young was also the editor of The Long Days or al-Ayyam al-Tawila, a six-hour Iraqi telenovela about the life of Saddam Hussein.
His wife was the novelist Dorothea Bennett. He died of a heart attack while working on a documentary at the age of 79 in Cannes.