Jessop began playing youth football with Glacis United, later moving across the border from Gibraltar to play for Linense's youth team Atlético Zabal before moving to San Roque. In April 2021 it was announced that he would move to England for the first time to join the Fleetwood Town International Football Academy at the end of the year.[1] His performances there led to a loan to Kendal Town being announced,[2][3] but registration issues caused the move to collapse. He instead joined Anchorsholme on loan in October 2022.[4]
After Anchorsholme folded at the end of the season, Jessop returned to Gibraltar to join FCB Magpies. However, after impressing for Gibraltar U19 in a pre-season friendly against the Chesterfield academy, the Spireites signed him that same summer.[5] He spent his first season playing for their academy side and their youth team in the eleventh tierCentral Midlands Alliance, but made his first team debut on 9 December 2023, scoring twice in a 6–1 win over Southport in the FA Trophy.[6] He made his first start a month later in the next round of the competition, as the Spireites fell to a 2–0 defeat to Welling United.[7] He made his league debut on 17 August 2024, in the EFL League Two win against Crewe Alexandra.[8]
International career
Jessop first represented Gibraltar at under-15 level, captaining the side in a 2019 UEFA Development Tournament.[9] In 2021 he stepped up to under-17 level, scoring on his debut in a 2–1 win over the Faroe Islands on 10 September. He made his under-21 debut just 2 months later, making a 3-minute cameo on 12 November 2021 in a 7–0 defeat to Wales.[10] He would become a regular fixture in the team 2 years later during the 2025 UEFA European Under-21 Championship qualification campaign, notably registering assists for Dylan Borge in the 3–1 defeat to Moldova on 15 June 2023[11] and for Tayler Carrington in the 2–1 victory against the same opponents on 21 November 2023.[12]