Maxwell began his career at Wrexham where he made his professional debut 18 years old in the 2008–09 season before moving to newly promoted League club Fleetwood Town in May 2012.
He made his Fleetwood Town and simultaneously his League debut during the 2013–14 season after successful loan spells at Wrexham and Cambridge United.
Maxwell has played internationally for Wales at under-21 level, and all other international age groups under-19, under-17 and under-16 schoolboys teams.
Born in St Asaph, Maxwell began his career coming through Wrexham's youth system, and signed a one-year professional contract in June 2008, which was extended under the management of Dean Saunders in January 2009, keeping him at the club until May 2010.
Maxwell spent a six-month loan spell at Welsh Premier League team Connah's Quay Nomads during the 2008–09 season, making 20 appearances in all competitions, before being called back by Wrexham in January 2009.
In April 2009, Maxwell made his professional debut at the age of 18 and went on to start the remaining 3 league games of the 2008–09 season, claiming his first senior clean sheet on the last day of the season against Weymouth.
After playing all of their 2009–10 pre-season games, Maxwell was joined at Wrexham by the more experienced Sam Russell. After only four games of the season, new signing Russell was sidelined with a dislocated elbow, allowing Maxwell the opportunity to start.
Maxwell went on to play 21 consecutive games and kept 10 clean sheets during Russell's absence. His contribution was acknowledged when he agreed an extension to his contract keeping him at the club until the end of the 2011 season. Maxwell regained the place ahead of Russell to play the last nine games of the season keeping a further five clean sheets. A number of defensive club records were broken; clean sheets, goals conceded and the first season where no more than two goals were conceded in a single game. Maxwell was recognised for his performances with a number of fans awards, including being named the Wrexham Football Association 'young player of the season'.
During the 2010–11 pre-season, Maxwell was joined at Wrexham by the more experienced Scott Shearer, and found himself once again fighting for the starting place. Maxwell took over the position in the starting line up just 10 games into the new season and soon started to attract the attention of higher league clubs. He cemented his claim to the number one position when Shearer left the club during the January transfer window.
Wrexham managed a play off spot but lost out to Luton Town in the semi final play-off games. Maxwell finished the season with a number of fans awards including the Wrexham Football Association 'young player of the season for the second year running.
Maxwell remained at Wrexham for the start of the 2011–12 season. After a frustrating season under new player manager Andy Morrell and starting only 11 times after losing the number one position to Joslain Mayebi , having been absent from the squad after being called up to the Wales under-21 side.
He decided he wanted to leave the club and was subsequently released.
Maxwell was immediately signed by newly promoted Football League newcomers, Fleetwood Town on 23 May 2012.
On Transfer deadline day in January 2013 Maxwell signed for his former club Wrexham on loan for the remainder of the 2012–13 season after first team goalkeeper Joslain Mayebi was ruled out with an injury for the rest of the season. Maxwell made his second Wrexham debut in a Conference Premier match away to Forest Green Rovers. In March 2013 Maxwell picked up his first career honour winning the FA Trophy at Wembley with Wrexham. Wrexham went on to play at Wembley a second time where they lost to Newport County in the Conference play off final.
Maxwell signed for Cambridge United on loan until January 2014 and quickly established himself as part of the team. Maxwell was handed the number 1 shirt by manager Richard Money despite being on loan and made his team debut on the first day of the 2013–14 season with a win against F.C. Halifax Town. The season started with a 16-game unbeaten run. This is a club record and with 11 clean sheets 6 of which were consecutive another club league record was established. Maxwell was awarded the Conference Premier player of the month for October after keeping 5 clean sheets and not conceding throughout the month, this involved saving a penalty as Cambridge beat Grimsby Town1–0 at Blundell Park. His loan with Cambridge ended on 6 January 2014 and he returned to Fleetwood Town. During his loan period, Maxwell kept a total of 18 clean sheets and conceded only 10 times during 24 league games.
After Cambridge failed to secure Maxwell's services for the remainder of the season Maxwell again returned to Highbury to battle both Scott Davies and David Lucas for the number one spot. Maxwell finally made his club and simultaneously his Football League debut under new manager Graham Alexander away from home against Wycombe Wanderers in a 1–1 draw on 11 February 2014 Maxwell retained his place for the remainder of the season helping Fleetwood to a fourth-place finish and a place in the League Two play off finals. Maxwell kept a total of 11 clean sheets in 22 games for Fleetwood bringing his season total to 29 in 50 games with 24 in 41 competitive league games. Fleetwood went on to win the play-off final at Wembley on 26 May, beating Burton Albion 1–0 in normal time. Following Fleetwood's promotion to League One, Maxwell signed a two-year contract extension with Fleetwood until the summer of 2016.
Fleetwood made an impressive start to the 2014–15 season with 10 points from the first 4 games good enough to top the league 1 table. Maxwell continued collecting clean sheets with 3 consecutive shut outs and only conceding 1 goal from a penalty in the season opener against Crewe Alexandra. Maxwell continued as the club number one and played every game during the season helping Fleetwood finish in 10th equal on points with Rochdale in 8th place. Only the top 3 clubs had a better defensive record. Maxwells efforts were recognised with a number of personal awards; Players Player, Supporters Player of the season and The Community Player of the season.
A change of strategic direction for the 2015–16 season saw the club fighting relegation for the entire season only securing League One status on the last day with a 2–0 win over already relegated Crewe Alexandra. Fleetwood eventually finish in 19th spot above relegated Fylde Coast rivals Blackpool. Despite being constantly in and out of the relegation zone only the top 7 clubs had a better defensive record.
Maxwell's effort were recognised with a number of personal awards; The PFA Community Player of the season, the League One unsung hero award for April 2016 and was a finalist in the North West MBNA Football awards for the 2014–15 season.
On 16 May 2016, Maxwell signed for Championship side Preston North End on a three-year deal, commencing 1 July 2016. He found himself competing for a starting place with Anders Lindegaard who returned to Preston following a loan spell during the previous season. He signed on a free transfer from West Bromwich Albion F.C.
Maxwell made his debut on 23 August in a 2–0 win against Oldham Athletic in the EFL Cup. He made his league debut on 23 September in a 1–0 win against Wigan Athletic.
Maxwell replaced Lindegaard as first choice for the remainder of the season, And was rewarded with a contract extension to 2020. At the end of the season, he was named Community Player of season at the club's annual awards.
Maxwell was joined by Declan Rudd who signed from Norwich at the start of the 2017/18 season as competition for the number 1 spot. Maxwell secured the starting place for the first game of the new season.
Maxwell is eligible to play for three home nations. He is Welsh by birth but has an English father and a Scottish grandfather.
He was a member of the U16 squad that won the 2005 Victory Shield, during the 2005–06 season, won his first U17 cap at the age of 15 and went on to win his first U19 cap at the age of just 16 and three days. During the 2008–09 season, Maxwell added a further two international age groups to his tally U23 semi professional and U21 honours both before his 19th birthday.
At the start of the 2009–10 season, Maxwell retained his place in the Wales U21 squad and played in all of Wales' Group 3 qualification games for the 2011 UEFA European Under-21 Football Championship. Maxwell continued as number 1 in the Wales U21 squad during 2010 and played in all of the remaining Wales' Group 3 qualification games for the 2011 UEFA European Under-21 Football Championship. Wales narrowly missed out on qualification for the next stage on an away goal rule to Italy. Maxwell continued to be a key member of the 2011–13 Wales U21 squad for qualification games in the 2013 UEFA European Under-21 Football Championship.
Maxwell was called into the senior side during the buildup to The 2016 Euro Championship in France due to an injury to Danny Ward. Maxwell remained with the squad during preparations but did not make the final squad when Ward made a full recovery.As of match played 12 September 2017
WrexhamFA Trophy: 2012–13
Fleetwood TownFootball League Two play-offs: 2013–14
InternationalVictory Shield: 2005
IndividualWrexham Football Association 'young player of the season'2009–10.
Wrexham Football Association 'young player of the season'2010–11.
Conference Premier Player of the Month: October 2013
Fleetwood Town Players' Player of the Season: 2014–15
Fleetwood Town Supporters' Player of the Season: 2014–15
Fleetwood Town Community Player of the Season: 2014–15
Fleetwood Town The PFA Community Player of the Season and Skybet league 1 unsung hero award for April: 2015–16
Preston North End Community Player of the season 2016-17