Webster joined Portsmouth at the age of 12, following rejections from Southampton, Chelsea and even Portsmouth from the age of ten. He signed academy scholarship with the club in the summer of 2011. He was first called up to the participate with the first team by Steve Cotterill in a friendly against FC Rostov. He came on in the 72nd minute for trialist Fernando Vega. Under the management of Michael Appleton, Webster was given more first team opportunities. Following an unused substitute appearance against Chelsea in the FA Cup, he made his debut at the age of 17 the following weekend in a Football League Championship match against West Ham United. He came on at right back in place of Greg Halford on the 75th minute. In the following season, Webster received the #22 jersey, and had more opportunities in first team, making his breakthrough as a full back. When recalled from Aldershot Town, he was put into the starting line up against Hartlepool United. Webster scored the only goal of the game, and his first senior goal, handing Portsmouth a 1–0 victory.
Aldershot Town (loan)
On 6 August 2013, Webster joined Aldershot Town on loan, until January 2014. He made his Shots debut four days later, in a 1–1 away draw against Grimsby. He returned to "Pompey" on 4 January, after making 21 appearances, and on the 21st he rejoined the "Shots" on loan until the end of the season.
On 6 June 2016, Webster moved to EFL Championship club Ipswich Town from Portsmouth for an undisclosed fee, in a deal which also saw defender Matt Clarke go in the opposite direction. He made his debut for the club on 6 August 2016, starting in a 4–2 home win over Barnsley at Portman Road. He scored his first goal for Ipswich against Birmingham City on 13 December 2016. Webster made 24 appearances in all competitions during the 2016–17 season, scoring once. Webster made his first appearance of the 2017–18 season on the opening day of the season in a 1–0 win over Birmingham City. He formed a defensive partnership with club captain Luke Chambers over the course of the season, making made 29 appearances in all competitions during his second season at the club.
On 28 June 2018, Webster transferred to fellow Football League Championship club Bristol City for an initial fee of £3.5 million rising up to £8 million.
Brighton & Hove Albion
On 2 August 2019, Brighton & Hove Albion agreed a fee of £20m rising up to £22m for Webster, subject to medical. On 3 August, Brighton completed the signing of Webster, signing him on a four-year deal. He made his debut 25 days later on the 27 August in a 2–1 away win against Bristol Rovers in the EFL Cup. Webster made his Premier League debut and league debut for The Seagulls starting in the 4–0 away loss to defending champions, Manchester City on the 31 August. On 5 October, Webster played the full match at home against Tottenham where he helped The Albion to a clean sheet in the 3–0 victory. Webster scored his first goal for The Seagulls and his first in the top flight on 19 October in a 2–1 defeat to Aston Villa at Villa Park. He netted again on 5 December opening the scoreline in an eventual 2–1 win over Arsenal. Throughout Webster's debut season for Brighton he kept his competition in Shane Duffy out of the starting 11 on a regular basis, starting in all 31 league appearances he played in scoring 3 goals, assisting 1 and recording 5 clean sheets.
International career
The same week he made his debut for Portsmouth, Webster was called up to the England U17's for a friendly tournament in Portugal. In October 2012, Webster was called up to the England U19, but his manager Michael Appleton blocked the requests from FA due to player shortage in Portsmouth. Later in the month, he was called up to England U18's. On 24 October 2012, Webster made his national team debut at under-18 level in a 2–0 win against Italy. On 13 November 2012 Webster made his England Under 19's debut in a 1–0 win over Finland, coming as a second-half substitute for Jack Stephens. On 24 May 2013, Webster made his 3rd appearance for the U19's coming on as a substitute in a match against Georgia.
