[6] On 2 February 2016 it was announced that Mepham had signed his first professional contract to be a member of the club's development squad and he finished his scholarship having made 43 appearances and scored two goals for the youth team.

[5][8][9][10] After consistently good performances for the reformed B team during the first half of the 2016–17 season, Mepham signed a two-year contract extension on 6 January 2017 and the following day,[11] he made his senior debut as a late substitute for Harlee Dean during a 5–1 FA Cup third round victory over Eastleigh.

[15] He made his first start for the club in a 3–1 EFL Cup third round defeat to Norwich City on 19 September 2017 and gave away the penalty which led to the Canaries' opening goal.

[16][17] After appearing sporadically throughout the autumn,[16] a head injury suffered by John Egan in December allowed Mepham a run in the team from the Christmas period until early February 2018.

[16][18] An achilles injury suffered by Andreas Bjelland in mid-March allowed Mepham back into the team and he scored the first senior goal of his career with the equaliser in a 1–1 draw with Sheffield United on Good Friday.

[16] Mepham began the 2018–19 season as the Bees' undisputed first-choice centre back in league matches, but was sent off for the first time in his career for two bookable offences committed during a 1–0 defeat to Bristol City on 20 October 2018.

[25] Mepham made a further ten appearances in the Premier League for the Cherries throughout the first half of the 2019–20 season, including a starring role in a 1–0 away win and clean sheet at Chelsea on 14 December.