Draper attended Parkside School in Stoke d’Abernon, Cobham, from age four to eleven, while being coached by Justin Sherring.

[4][5] Draper reached his first and only junior Grand Slam final at the 2018 Wimbledon Championships, where he lost to Tseng Chun-hsin in three sets.

[citation needed] Plagued by injuries for most of his career, Draper made his ATP Tour main draw debut in singles as a wildcard at the Miami Open.

[7] At the Queen's Club Championships in June, Draper secured the biggest win of his career to date with a victory over world No.

39 Alexander Bublik in the round of 16 to reach the quarterfinals of an ATP tournament for the first time in his career, where he lost to eventual finalist Cameron Norrie.

[13] Two weeks later, Draper continued his run of form at the Città di Forlì IV, where he was unseeded and reached his second final to claim his second Challenger title after defeating Tim van Rijthoven, 6–1, 6–2.

[17] Draper went on the next week to win his fourth Challenger title at Saint-Brieuc, defeating Zizou Bergs in the final.

[22] He earned a direct entry at a major tournament for the first time at the 2022 Wimbledon Championships and won his first Grand Slam match defeating wildcard Zizou Bergs.

[23][24] Draper qualified for the Canadian Open in Montreal, where, after beating Hugo Gaston in the first round, upset third seed and world No.

[26] After Gaël Monfils, his third-round opponent, retired due to injury, Draper advanced to his first Masters 1000 quarterfinal.

[35] At the NextGen Finals he reached the semifinals defeating top seed Lorenzo Musetti in the group stage.

[46] He made his debut at the 2023 French Open but was forced to retire from his first round match against Tomás Martín Etcheverry due to a shoulder injury.

[47] Draper made his return to the ATP Tour during the US Open where he defeated Radu Albot, 17th seed Hubert Hurkacz and Michael Mmoh to advance to the second week.

82 at the next tournament, the 2023 Sofia Open, he reached his second semifinal of the season defeating top seed Lorenzo Musetti[52] and qualifier Cem Ilkel.

[60] He reached the semifinals at an ATP 500 event for the first time at the 2024 Abierto Mexicano Telcel in Acapulco defeating sixth seed Tommy Paul,[61] lucky loser Yoshihito Nishioka[62] and Miomir Kecmanovic.

[65] Draper reached his third career final at the 2024 BOSS Open in Stuttgart defeating three Americans en route, Marcos Giron,[66] defending champion and fourth seed Frances Tiafoe[67][68] and Brandon Nakashima.

[69] Draper beat Matteo Berrettini in the final to lift his maiden title, making him the eighth first-time ATP Tour champion for 2024.

[72][73] At the next grass court tournament, the 2024 Queen's Club Championships the following week, he reached back-to-back quarterfinals defeating Mariano Navone[74] and top seed and defending champion Carlos Alcaraz, in straight sets.

[77] At Wimbledon, Draper defeated Swedish qualifier Elias Ymer in five sets in the first round[78] but lost his next match to compatriot Cameron Norrie.

[79] On 15 July, he was named in the Great Britain squad for the Davis Cup group stage to be held in Manchester in September.

[80][81] At the 2024 Summer Olympics in Paris, Draper defeated Kei Nishikori in the first round,[82][83] before losing to seventh seed Taylor Fritz in three sets.

[84] At the 2024 Cincinnati Open he reached the round of 16 for the first time at the tournament, with an upset over ninth seed Stefanos Tsitsipas.

[96] At the Japan Open he reached the quarterfinals, defeating qualifier Mattia Bellucci[97] and upsetting second seed Hubert Hurkacz, his third top 10 win of the season.

[99] Draper returned to the court three weeks later at the Vienna Open where he defeated Kei Nishikori,[100] Luciano Darderi,[101] Tomas Machac[102][103] and sixth seed Lorenzo Musetti to make it through to the final[104][105] where he overcame Karen Khachanov in straight sets to claim his first ATP 500 title.

[119] Draper is coached by James Trotman at the National Tennis Centre in Roehampton as part of the LTA's Elite Players support programme.