Born in Westminster, Baxter began his career with Cray Wanderers. He then joined Chelsea at the age of 8. In the 2015–16 season he won the FA Youth Cup and the UEFA Youth League. In August 2016 he moved on loan to Isthmian League side Metropolitan Police on a short-term deal until January 2017. He spent four months at the club, making 19 appearances, before returning to Chelsea in January 2017. He then joined National League side Solihull Moors on loan for the remainder of the 2016–17 campaign. On 21 January 2017, he made his Solihull debut, keeping a clean sheet during their 0–0 draw with Boreham Wood. He made three clean sheets in his first four games for the club. Baxter went onto appear 17 appearances in total for the club. On 21 June 2017, Baxter joined fellow National League side Woking on a season-long loan. On the opening day of the campaign, Baxter went onto make his Woking debut as they recorded a 2–1 home victory over Gateshead. Baxter went on to make 48 appearances in total for the club. During the 2017–18 season, Baxter played more minutes than any other Chelsea loanee. On 26 June 2018, Baxter agreed to join League Two side Yeovil Town on a season-long loan. Baxter made his Football League debut in their opening day of the season, in a 1–0 away defeat against Bury. At Yeovil, he did not concede a goal for 10 hours 12 minutes, and set a club record after keeping 6 consecutive clean sheets in all competitions. As of 5 November 2018, he was the "only teenage goalkeeper currently in English football's professional ranks to have racked up over 100 appearances in the senior game". Baxter made 38 appearances for Yeovil during his season with the club, and won 5 awards at the club's end of season awards, all in the 'Player of the Season' and 'Young Player of the Season' categories. On 19 June 2019, Baxter joined Scottish Premiership sideRoss County on a season long loan. He suffered a shoulder injury early in the season before returning to first-team action, and as of 13 February 2020 had played in 14 games in a row.
Career statistics
Personal life
Baxter has stated that Petr Čech was his inspiration.
