[5] After performing well for both the under-18s and under-21s, he made his first team debut for the club as a substitute in their 2–0 loss against Leicester City at the John Smith's Stadium on 26 April 2014.

His first goal for the club came from a 30-yard strike against Nottingham Forest at the City Ground in a 2–0 win for the Terriers on 13 February 2016.

[7] On 19 November 2016, he scored his second goal for the club with a volley from 32 yards out in a 3–2 loss against Cardiff City.

[11] In March 2019, Billing suffered racial abuse on social media; the matter was reported to police.

[12] On 29 July 2019, Billing signed for Premier League AFC Bournemouth on a long-term contract for a £15 million fee.

[15] Billing scored his first goals for the club in the FA Cup third round fixture against Luton Town, as Bournemouth won the game 4–0.

[21] On 16 December 2023, during a Premier League match against Luton Town, Billing was the first person to summon assistance to opponent player Tom Lockyer, who had suffered a cardiac arrest on the pitch, before the arrival of the medical staff; following Lockyer's discharge from the hospital, Luton publicly thanked Billing in an official press statement.

[28] He earned his first cap for the Danish U21 team in a qualifying match for the 2019 European Championship against the Faroe Islands on 31 August 2017.