Baxter is a product of the Chelsea youth system having joined the club in 2006 at the age of eight. 

Between the years of 2016 and 2023, Baxter experienced eight loan spells with seven different clubs and made a step up with each stint.

His first loan move was at the Metropolitan Police followed by Solihull, Woking, Yeovil, Ross County, Acrrington Stanley and finally Hull in the Sky Bet Championship.

In the summer of 2023, Wanderers signed the highly-rated keeper on a two-year contract, his first permanent move away from Chelsea.