Wisdom was born in Leeds but it was Bradford City who spotted his potential in local junior football and invited him to join their youth set-up. It wasn't long before bigger clubs were showing an interest in the defender and Liverpool made their move in January 2008 when Wisdom was still only fourteen years old. The fee that Liverpool paid was undisclosed but it is believed that Bradford City were properly compensated for losing one of their outstanding young players.
Gary Ablett was so impressed with what Wisdom had to offer that he picked him in a squad for a reserve match soon after the youngster’s fifteenth birthday. Although officially an Under-16 player, Wisdom became a regular for the Under-18s and was an important part of the team that reached the FA Youth Cup Final in 2009, only to lose to Arsenal over two legs. He proved his versatility during this period of his development, being as comfortable at full-back as he was as a central defender. Wisdom was also being closely watched by the England staff. He won the Victory Shield with England’s Under-16 team in 2008 and took part in the Under-17 European championships in Liechtenstein in May 2010. England reached the final to face Spain. Midway through the first half a shot deflected into the England net off young Wisdom but he recovered his composure immediately, so much so that eight minutes later he strode upfield to head the equalising goal from a corner. A couple of minutes before half-time Conor Wickham guaranteed England’s first age-group title since 1993, the cup being collected by Conor Coady, Wisdom's captain at their club as well as at international level.
Incoming manager Roy Hodgson was quickly aware that he had a very promising player available to him and Wisdom was allocated the Number 47 shirt in his first-team squad. Wisdom's reward for his progress was a place on the bench in the club's final Premier League match of the season at Aston Villa in May 2011. Yet Wisdom didn't figure in a senior matchday squad in 2011/12. Martin's Kelly injury early on in the 2012/13 season opened the first-team door for Wisdom under new boss Brendan Rodgers. Wisdom started nineteen matches duting that campaign but most of those came in the first half of the season. He scored on his debut against Young Boys of Bern in the Europa League in September, a powerful header direct from a corner that restored Liverpool's lead at 2-1.
Two days after helping Liverpool to defeat defending League champions Manchester United at Anfield on 1 September 2013, Wisdom was named as captain of England's Under-21 team by incoming manager Gareth Southgate, who had replaced Stuart Pearce in that position. The 20-year-old joined the Rams in October on a temporary deal. Before this transaction took place Rodgers revealed he would have loaned him earlier if it had not been for the injury to Glen Johnson.
Wisdom was a big success at Derby. He played in 34 matches during the regular Championship season plus both the play-off semi-final matches against Brighton which Derby won 6-2 on aggregate to qualify for the play-off final against Queens Park Rangers. Wisdom also played for Derby against Chelsea in the FA Cup. He celebrated his 21st birthday shortly before the end of the season. He featured in the Championship play-off final at Wembley against QPR on 24 May 2014. But it was the London club that reached the Premier League with a last-minute goal so Wisdom's time with Derby ended in great disappointment.
The young defender spent the 2014/15 season on loan at Premier League club West Bromwich Albion where he played in 24 of Albion's 38 Premier League matches. He also appeared once in the FA Cup and once in the Football League Cup. Wisdom was loaned for the third season running in the summer of 2015, this time to Premier League side Norwich City for the 2015/16 season, so he is clearly not deemed ready for Liverpool's first team. Again Wisdom moved in the summer of 2016, this time loaned to Red Bull Salzburg where former Liverpool boss, Gérard Houllier is Global Sports Director. He finally completed a permanent move away from Anfield at the beginning of July 2017 when he joined Championship side Derby County and played thirty league games for them that season. However under Frank Lampard in 2018/19 he fell out of favour and made just eleven appearances. Lampard left to take over at Chelsea in the summer of 2019 but Wisdom had to be patient under new boss Philip Cocu. He didn't start a league game until the end of November but did force his way back into the starting line-up, captaining the side on one occasion. However he was forced to miss the last seven games of the Covid 19 delayed season when he was stabbed in the head and buttocks as he was robbed during a visit to friends in Liverpool. He did make a full recovery for the start of the 2020/21 campaign and played 38 times that season. He was then out of contract in the summer and with Derby's financial problems well documented, a new agreement could not be reached. He became a free agent but despite his versatility failed to find a club during the transfer window.