Born in Portsmouth, Close signed a two-year scholarship deal after spending many years in Portsmouth's youth categories.[3] He was an unused substitute for a first team game on 3 May 2014 for a league game against Plymouth Argyle.[5]
Close made his League Two debut on 16 September, again from the bench in a 3–0 home success against Dagenham & Redbridge.[8] After playing only 4 games for Pompey in 2016–17, on 31 January 2017, he joined National League side Eastleigh on loan until the end of the season.[9]
On 26 May 2017 Close signed a new one-year contract at Pompey, with the club holding an option for an additional year.[10] On 17 December, after becoming a starter under new manager Kenny Jackett, he extended his contract until 2020.[11]
On 2 March 2019, Close scored his first professional brace in a 5–1 home victory over Bradford City.[12]