Born in Bedford, Bedfordshire, Musonda joined Luton Town in 2006 aged eight and progressed through the club's youth system. During his time in the club's academy he played in numerous positions, including as a striker, before settling on a central defensive role. He was part of the under-11 team which defeated Bayern Munich 3–2 to win the Aarau Masters in 2009. Musonda was promoted to Luton's under-18 team as a first year scholar in 2014 and was named captain. He began 2015–16 playing for both the under-18 team and the development squad alongside senior professionals. After leading the under-18's on a 16-match unbeaten run, during which the team conceded only seven goals, he signed a one-and-a-half-year professional contract with Luton on 4 November 2015. Musonda continued to captain the under-18 team which went on to win the Youth Alliance South East title and the Youth Alliance Cup, and also reached the quarter-finals of the FA Youth Cup, in which they lost 1–0 to Blackburn Rovers. Musonda first became involved with the Luton first-team when he was named on the bench on his eighteenth birthday for a League Two match against Northampton Town, though he remained an unused substitute. On 23 January 2016, Musonda was introduced as a 94th-minute substitute for Pelly Ruddock Mpanzu in a 2–0 win away to Mansfield Town to make his professional debut. He made his second appearance of the season on 9 April, coming on as an 85th-minute substitute for Dan Potts in a 2–0 defeat at home to Accrington Stanley. Musonda was introduced as an 89th-minute substitute for Jake Howells in Luton's final match of the season, a 4–1 win at home to Exeter City. Musonda scored his first professional goal on his first appearance of 2016–17 in a 2–1 win away to Gillingham in the EFL Trophy on 30 August 2016. He made four further appearances in the EFL Trophy, before joining National League club Braintree Town on 3 March 2017 on an initial one-month loan. Having made his debut a day later in a 2–1 home defeat to Wrexham, Musonda finished his loan spell at Braintree with three appearances. Shortly after the start of 2017–18, Musonda signed a new contract with Luton on 9 August 2017 to keep him at the club until the summer of 2019, with the option of a further year. He joined National League South club Oxford City on 9 February 2018 on a one-month youth loan and made his debut after starting in a 4–1 home win over Hemel Hempstead Town a day later. The loan was extended on 16 March until the end of the season. Musonda made 13 appearances and scored one goal as Oxford finished 16th in the National League South. His contract with Luton was extended by a further year at the end of the season after a promotion clause was triggered as a result of the club's promotion to League One. He rejoined Oxford City on 26 October 2018 on loan for a month. Musonda's second loan spell with Oxford ended having scored one goal from seven appearances. He was loaned to another National League South club, Hemel Hempstead Town, on 9 January 2019 until the end of 2018–19. Musonda joined St AlbansCity of the National League South on 18 October 2019 on loan until January 2020. His debut came a day later in a 1–0 home defeat to Bath City and made 12 further appearances, completing the loan with 13 appearances and one goal before returning to Luton. He returned to St Albans on 6 March 2020 on loan until the end of the season.
