Stone played as a centre-half in his youth until he put on extra weight at the age of 14 and decided to concentrate on goalkeeping.[5] He played for Sporting Khalsa.[6] Having failed a three-month trial spell at Walsall at the age of 16, he joined Midland League side Brocton in February 2016, winning the club's young player and players' Player of the Year awards during the 2016–17 Premier Division relegation campaign.[7][6] He won a total of six caps for the England Schoolboys U18s team in 2017, playing against Northern Ireland and Australia in England's victorious Centenary Shield campaign.[6][3][8]
He made 24 appearances in the 2020–21 season and was praised by manager Nigel Clough in April for recovering from a costly error in a 1–1 draw with Newport County to pick up the man of the match award for his performance in a 1–0 win at Stevenage.[22] The following month he was named as the club's Football in the Community's PFA Community Champion for his championing of a healthy eating campaign with Wynndale Primary School.[23] However, the club confirmed that Stone would not be offered a new contract.[24] Stone described the decision as "a bit of a shock" as "I thought I'd done enough to earn a new contract".[25]
Port Vale
Stone in goal for Port Vale (November 2021)
On 25 June 2021, Port Vale announced that they had signed Stone on a one-year deal to start on 1 July, with the option of a further 12 months; manager Darrell Clarke said that "we are pleased to have secured Aidan's future at Vale Park and expect to have a healthy dose of competition now in the goalkeeping positions, following Lucas Covolan's arrival earlier in the week."[26] He was given the chance to secure a starting place after Covolan was sent off on the opening day of the 2021–22 season.[27] Covolan was returned to the starting eleven upon serving his suspension, only to be sent off yet again in January; Stone had to then sit on the bench behind new loan signing Tomáš Holý until giving an impressive performance upon being given his first league start in two months on 12 March.[28] He remained in goal for the rest of the season and saved three penalties in the penalty shoot-out victory over Swindon Town in the play-off semi-final.[29] He started in the play-off final at Wembley Stadium as Vale secured promotion with a 3–0 victory over Mansfield Town; Michael Baggaley of The Sentinel wrote that "[Stone had an] early mix up with Gibbons but retrieved the situation with a save from Murphy... spilled a ball into the area but Hall cleared off the line.... [Stone] has played a huge part in getting Vale this far".[30][31] The club named him as Young Player of the Year and invoked their option to extend his contract by a further 12 months in June 2022.[32][33] The club then gave Stone a new deal to run until 2024.[34]
He lost his first-team spot to loan signing Jack Stevens early in the 2022–23 campaign, with Clarke claiming that further work with coachCarlo Nash would bring out Stone's potential as a "top half of League One goalie".[35] Stevens remained first-choice goalkeeper for much of the campaign, though Stone was returned to the first XI in February, at which stage Clarke said that there was little to choose between the two.[36] Stone ended the campaign with 26 appearances, twenty of which were in the league.[37] He was permitted to leave the club on a free transfer after Port Vale signed Connor Ripley from Morecambe.[38]
Notts County
On 23 June 2023, Stone signed a two-year deal with League Two club Notts County, where he would compete with Sam Slocombe for a first-team place.[39] He was sent off on his debut for the club as County were beaten 5–1 at Sutton United on the opening day of the 2023–24 season; he had brought down Scott Kashket following a poor back-pass.[40] He was transfer-listed at the end of the season by new head coach Stuart Maynard.[41]
